75:@0.922460:0.966765:0.939432:0.966765:0.939432:0.950778:0.922460:0.950778:0.000000:0.000000
Ejercicios resueltos:@0.108233:0.096570:0.238888:0.096570:0.238888:0.079783:0.108233:0.079783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.108233:0.113762:0.120505:0.113762:0.120505:0.097047:0.108233:0.097047:0.000000:0.000000
  Sea   = (4, 3). Entonces,   ∙   = (4)  + (3)  = 25. Luego, :@0.120506:0.113545:0.519146:0.113545:0.519146:0.097047:0.120506:0.097047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.160230:0.113661:0.171500:0.113661:0.171500:0.097192:0.160230:0.097192:0.000000
:@0.163312:0.111521:0.169728:0.111521:0.169728:0.095703:0.163312:0.095703:0.000000
A A:@0.304816:0.113661:0.337779:0.113661:0.337779:0.097192:0.304816:0.097192:0.000000:0.000000:0.000000
 :@0.307898:0.111521:0.336006:0.111521:0.336006:0.095703:0.307898:0.095703:0.000000:0.000000:0.000000
2:@0.376660:0.107193:0.381613:0.107193:0.381613:0.097575:0.376660:0.097575:0.000000
2:@0.421106:0.107193:0.426059:0.107193:0.426059:0.097575:0.421106:0.097575:0.000000
|| || =    (  ·  ) =    25 = 5.:@0.131975:0.138025:0.320755:0.138025:0.320755:0.121527:0.131975:0.121527:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.144304:0.138140:0.155574:0.138140:0.155574:0.121672:0.144304:0.121672:0.000000
:@0.147387:0.136000:0.153802:0.136000:0.153802:0.120182:0.147387:0.120182:0.000000
A A:@0.203603:0.138140:0.236566:0.138140:0.236566:0.121672:0.203603:0.121672:0.000000:0.000000:0.000000
 :@0.206685:0.136000:0.234793:0.136000:0.234793:0.120182:0.206685:0.120182:0.000000:0.000000:0.000000
2.:@0.108240:0.172943:0.120512:0.172943:0.120512:0.156228:0.108240:0.156228:0.000000:0.000000
  Si   = (0, 0), entonces   ∙   = 0, y ||   || =    (  ·  ) =    0  = 0.:@0.120511:0.172726:0.552631:0.172726:0.552631:0.156228:0.120511:0.156228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.147926:0.172842:0.159196:0.172842:0.159196:0.156373:0.147926:0.156373:0.000000
:@0.151009:0.170702:0.157424:0.170702:0.157424:0.154884:0.151009:0.154884:0.000000
A A:@0.290373:0.172842:0.323336:0.172842:0.323336:0.156373:0.290373:0.156373:0.000000:0.000000:0.000000
 :@0.293456:0.170702:0.321564:0.170702:0.321564:0.154884:0.293456:0.154884:0.000000:0.000000:0.000000
A:@0.381402:0.172842:0.392672:0.172842:0.392672:0.156373:0.381402:0.156373:0.000000
:@0.384484:0.170702:0.390900:0.170702:0.390900:0.154884:0.384484:0.154884:0.000000
A A:@0.441760:0.172842:0.474723:0.172842:0.474723:0.156373:0.441760:0.156373:0.000000:0.000000:0.000000
 :@0.444842:0.170702:0.472950:0.170702:0.472950:0.154884:0.444842:0.154884:0.000000:0.000000:0.000000
Distancia entre dos puntos :@0.108233:0.208825:0.327350:0.208825:0.327350:0.191142:0.108233:0.191142:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.108233:0.225995:0.188317:0.225995:0.188317:0.209050:0.108233:0.209050:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean   = ( ,  ),   = ( ,  )    . Se llama distancia de   a :@0.188319:0.225533:0.599913:0.225533:0.599913:0.209035:0.188319:0.209035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.233284:0.225648:0.244554:0.225648:0.244554:0.209180:0.233284:0.209180:0.000000
:@0.236386:0.223509:0.242801:0.223509:0.242801:0.207690:0.236386:0.207690:0.000000
a b B:@0.269271:0.225648:0.316741:0.225648:0.316741:0.209180:0.269271:0.209180:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.309516:0.223509:0.315932:0.223509:0.315932:0.207690:0.309516:0.207690:0.000000
c d:@0.343173:0.225648:0.366580:0.225648:0.366580:0.209180:0.343173:0.209180:0.000000:0.000000:0.000000
:@0.376809:0.225014:0.391462:0.225014:0.391462:0.211641:0.376809:0.211641:0.000000
:@0.395744:0.224446:0.409049:0.224446:0.409049:0.211584:0.395744:0.211584:0.000000
2:@0.409049:0.219180:0.414002:0.219180:0.414002:0.209562:0.409049:0.209562:0.000000
A:@0.572960:0.225648:0.584231:0.225648:0.584231:0.209180:0.572960:0.209180:0.000000
:@0.576081:0.223509:0.582497:0.223509:0.582497:0.207690:0.576081:0.207690:0.000000
B:@0.108244:0.242999:0.117433:0.242999:0.117433:0.226530:0.108244:0.226530:0.000000
:@0.110209:0.240859:0.116624:0.240859:0.116624:0.225041:0.110209:0.225041:0.000000
, que se nota  ( ,  ), al número real no negativo:@0.118551:0.242884:0.459351:0.242884:0.459351:0.226386:0.118551:0.226386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d A B:@0.212814:0.242999:0.254679:0.242999:0.254679:0.226530:0.212814:0.226530:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.231021:0.240859:0.253870:0.240859:0.253870:0.225041:0.231021:0.225041:0.000000:0.000000:0.000000
d A B:@0.206420:0.277701:0.248283:0.277701:0.248283:0.261232:0.206420:0.261232:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ) = ||  –  || =    (  –  )  + (  –  )  .:@0.215590:0.277585:0.497597:0.277585:0.497597:0.261087:0.215590:0.261087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.224625:0.275561:0.247474:0.275561:0.247474:0.259743:0.224625:0.259743:0.000000:0.000000:0.000000
A B:@0.284463:0.277701:0.323090:0.277701:0.323090:0.261232:0.284463:0.261232:0.000000:0.000000:0.000000
:@0.287546:0.275561:0.293961:0.275561:0.293961:0.259743:0.287546:0.259743:0.000000
:@0.315866:0.275561:0.322281:0.275561:0.322281:0.259743:0.315866:0.259743:0.000000
a c:@0.371696:0.277701:0.406643:0.277701:0.406643:0.261232:0.371696:0.261232:0.000000:0.000000:0.000000
2:@0.412576:0.271232:0.417529:0.271232:0.417529:0.261614:0.412576:0.261614:0.000000
b d:@0.442574:0.277701:0.479795:0.277701:0.479795:0.261232:0.442574:0.261232:0.000000:0.000000:0.000000
2:@0.485747:0.271232:0.490700:0.271232:0.490700:0.261614:0.485747:0.261614:0.000000
Ejercicio resuelto:@0.108227:0.312662:0.226206:0.312662:0.226206:0.295876:0.108227:0.295876:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.108227:0.329854:0.120499:0.329854:0.120499:0.313140:0.108227:0.313140:0.000000:0.000000
  Los vértices de un triángulo son los vértices   = (–2, 1),   = (1, 2), :@0.120499:0.329637:0.599895:0.329637:0.599895:0.313140:0.120499:0.313140:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.444054:0.329753:0.455325:0.329753:0.455325:0.313284:0.444054:0.313284:0.000000
:@0.447141:0.327613:0.453556:0.327613:0.453556:0.311795:0.447141:0.311795:0.000000
B:@0.527458:0.329753:0.536647:0.329753:0.536647:0.313284:0.527458:0.313284:0.000000
:@0.529423:0.327613:0.535838:0.327613:0.535838:0.311795:0.529423:0.311795:0.000000
C:@0.131961:0.347104:0.141998:0.347104:0.141998:0.330635:0.131961:0.330635:0.000000
:@0.135256:0.344964:0.141671:0.344964:0.141671:0.329146:0.135256:0.329146:0.000000
 = (2, –3). Calculemos el perímetro del triángulo de la Figura 2.9.:@0.141671:0.346988:0.593360:0.346988:0.593360:0.330490:0.141671:0.330490:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108226:0.381690:0.112368:0.381690:0.112368:0.365192:0.108226:0.365192:0.000000
Para el efecto, calculemos las longitudes de cada uno de los lados :@0.131961:0.381690:0.599851:0.381690:0.599851:0.365192:0.131961:0.365192:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del triángulo. Tenemos:@0.131961:0.399040:0.292978:0.399040:0.292978:0.382543:0.131961:0.382543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108226:0.433742:0.112368:0.433742:0.112368:0.417244:0.108226:0.417244:0.000000
A B:@0.131961:0.433857:0.170588:0.433857:0.170588:0.417389:0.131961:0.417389:0.000000:0.000000:0.000000
:@0.135044:0.431718:0.141459:0.431718:0.141459:0.415899:0.135044:0.415899:0.000000
 –   = (–2, 1) – (1, 2) = (–3, –1),:@0.142615:0.433742:0.370311:0.433742:0.370311:0.417244:0.142615:0.417244:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.163364:0.431718:0.169779:0.431718:0.169779:0.415899:0.163364:0.415899:0.000000
 :@0.108226:0.451093:0.112368:0.451093:0.112368:0.434595:0.108226:0.434595:0.000000
A C:@0.131961:0.451208:0.171436:0.451208:0.171436:0.434739:0.131961:0.434739:0.000000:0.000000:0.000000
:@0.135044:0.449068:0.141459:0.449068:0.141459:0.433250:0.135044:0.433250:0.000000
 –   = (–2, 1) – (2, –3) = (–4, 4),:@0.142615:0.451093:0.369714:0.451093:0.369714:0.434595:0.142615:0.434595:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.164693:0.449068:0.171108:0.449068:0.171108:0.433250:0.164693:0.433250:0.000000
 :@0.108226:0.468443:0.112368:0.468443:0.112368:0.451946:0.108226:0.451946:0.000000
B:@0.131961:0.468559:0.141151:0.468559:0.141151:0.452090:0.131961:0.452090:0.000000
:@0.133926:0.466419:0.140342:0.466419:0.140342:0.450601:0.133926:0.450601:0.000000
 –   = (1, 2) – (2, –3) = (–1, 5),:@0.142268:0.468443:0.358867:0.468443:0.358867:0.451946:0.142268:0.451946:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.161052:0.468559:0.171089:0.468559:0.171089:0.452090:0.161052:0.452090:0.000000
:@0.164346:0.466419:0.170761:0.466419:0.170761:0.450601:0.164346:0.450601:0.000000
 :@0.108226:0.485794:0.112368:0.485794:0.112368:0.469296:0.108226:0.469296:0.000000
 :@0.108226:0.503145:0.112368:0.503145:0.112368:0.486647:0.108226:0.486647:0.000000
y de la definición de distancia entre dos puntos, obtenemos::@0.131961:0.503145:0.558642:0.503145:0.558642:0.486647:0.131961:0.486647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108226:0.537846:0.112368:0.537846:0.112368:0.521349:0.108226:0.521349:0.000000
d A B:@0.131961:0.537962:0.173825:0.537962:0.173825:0.521493:0.131961:0.521493:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ) = ||  –  || =    9 + 1  =    10 ,:@0.141131:0.537846:0.385376:0.537846:0.385376:0.521349:0.141131:0.521349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.150167:0.535822:0.173015:0.535822:0.173015:0.520004:0.150167:0.520004:0.000000:0.000000:0.000000
A B:@0.210005:0.537962:0.248632:0.537962:0.248632:0.521493:0.210005:0.521493:0.000000:0.000000:0.000000
:@0.213087:0.535822:0.219502:0.535822:0.219502:0.520004:0.213087:0.520004:0.000000
:@0.241407:0.535822:0.247822:0.535822:0.247822:0.520004:0.241407:0.520004:0.000000
 :@0.108226:0.562325:0.112368:0.562325:0.112368:0.545827:0.108226:0.545827:0.000000
d A C:@0.131961:0.562440:0.174672:0.562440:0.174672:0.545972:0.131961:0.545972:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ) = ||  –  || =    16 + 16  = 4   2 ,:@0.141131:0.562325:0.403293:0.562325:0.403293:0.545827:0.141131:0.545827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.150167:0.560300:0.174345:0.560300:0.174345:0.544482:0.150167:0.544482:0.000000:0.000000:0.000000
A C:@0.211141:0.562440:0.250616:0.562440:0.250616:0.545972:0.211141:0.545972:0.000000:0.000000:0.000000
:@0.214224:0.560300:0.220639:0.560300:0.220639:0.544482:0.214224:0.544482:0.000000
:@0.243873:0.560300:0.250288:0.560300:0.250288:0.544482:0.243873:0.544482:0.000000
 :@0.108226:0.586804:0.112368:0.586804:0.112368:0.570307:0.108226:0.570307:0.000000
d B C:@0.131961:0.586920:0.174325:0.586920:0.174325:0.570451:0.131961:0.570451:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ) = ||  –  || =    1 + 25  =    26 .:@0.141131:0.586804:0.395452:0.586804:0.395452:0.570307:0.141131:0.570307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.149049:0.584780:0.173998:0.584780:0.173998:0.568962:0.149049:0.568962:0.000000:0.000000:0.000000
B:@0.210795:0.586920:0.219984:0.586920:0.219984:0.570451:0.210795:0.570451:0.000000
:@0.212760:0.584780:0.219175:0.584780:0.219175:0.568962:0.212760:0.568962:0.000000
C:@0.239885:0.586920:0.249922:0.586920:0.249922:0.570451:0.239885:0.570451:0.000000
:@0.243179:0.584780:0.249595:0.584780:0.249595:0.568962:0.243179:0.568962:0.000000
 :@0.108226:0.624108:0.112368:0.624108:0.112368:0.607611:0.108226:0.607611:0.000000
En consecuencia, el perímetro   es::@0.131961:0.624108:0.378959:0.624108:0.378959:0.607611:0.131961:0.607611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.348135:0.624224:0.357401:0.624224:0.357401:0.607755:0.348135:0.607755:0.000000
 :@0.108226:0.641459:0.112368:0.641459:0.112368:0.624962:0.108226:0.624962:0.000000
p d A B:@0.131961:0.641575:0.202183:0.641575:0.202183:0.625106:0.131961:0.625106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 =  ( ,  ) +  ( ,  ) +  ( ,  ) =   10 + 4   2 +   26 .:@0.141228:0.641459:0.493108:0.641459:0.493108:0.624962:0.141228:0.624962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.178525:0.639435:0.201374:0.639435:0.201374:0.623617:0.178525:0.623617:0.000000:0.000000:0.000000
d A C:@0.228345:0.641575:0.271056:0.641575:0.271056:0.625106:0.228345:0.625106:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.246551:0.639435:0.270729:0.639435:0.270729:0.623617:0.246551:0.623617:0.000000:0.000000:0.000000
d B C:@0.297507:0.641575:0.339872:0.641575:0.339872:0.625106:0.297507:0.625106:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.314596:0.639435:0.339544:0.639435:0.339544:0.623617:0.314596:0.623617:0.000000:0.000000:0.000000
 :@0.108226:0.658810:0.112368:0.658810:0.112368:0.642312:0.108226:0.642312:0.000000
Ortogonalidad:@0.108233:0.677557:0.227320:0.677557:0.227320:0.659874:0.108233:0.659874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i):@0.108233:0.694482:0.118771:0.694482:0.118771:0.677767:0.108233:0.677767:0.000000:0.000000
  Sean  ,     :@0.118771:0.694265:0.224832:0.694265:0.224832:0.677767:0.118771:0.677767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.171192:0.694380:0.199358:0.694380:0.199358:0.677912:0.171192:0.677912:0.000000:0.000000:0.000000
 :@0.174274:0.692240:0.198549:0.692240:0.198549:0.676422:0.174274:0.676422:0.000000:0.000000:0.000000
:@0.206039:0.693746:0.220691:0.693746:0.220691:0.680373:0.206039:0.680373:0.000000
:@0.226254:0.693178:0.239558:0.693178:0.239558:0.680316:0.226254:0.680316:0.000000
2:@0.239558:0.687912:0.244512:0.687912:0.244512:0.678294:0.239558:0.678294:0.000000
. Se dice que   es ortogonal o perpendicular a    :@0.244512:0.694265:0.599918:0.694265:0.599918:0.677767:0.244512:0.677767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.342245:0.694380:0.353515:0.694380:0.353515:0.677912:0.342245:0.677912:0.000000
:@0.345308:0.692240:0.351723:0.692240:0.351723:0.676422:0.345308:0.676422:0.000000
B:@0.587412:0.694380:0.596602:0.694380:0.596602:0.677912:0.587412:0.677912:0.000000
:@0.589360:0.692240:0.595776:0.692240:0.595776:0.676422:0.589360:0.676422:0.000000
que se escribe       si y solo si   ·   = 0. Sean       y       :@0.131984:0.711615:0.599908:0.711615:0.599908:0.695118:0.131984:0.695118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.237862:0.711731:0.249132:0.711731:0.249132:0.695262:0.237862:0.695262:0.000000
:@0.240948:0.709591:0.247363:0.709591:0.247363:0.693773:0.240948:0.693773:0.000000
:@0.253316:0.710647:0.269364:0.710647:0.269364:0.697200:0.253316:0.697200:0.000000
B:@0.274161:0.711731:0.283351:0.711731:0.283351:0.695262:0.274161:0.695262:0.000000
:@0.276126:0.709591:0.282542:0.709591:0.282542:0.693773:0.276126:0.693773:0.000000
A B:@0.365958:0.711731:0.398133:0.711731:0.398133:0.695262:0.365958:0.695262:0.000000:0.000000:0.000000
 :@0.369023:0.709591:0.397324:0.709591:0.397324:0.693773:0.369023:0.693773:0.000000:0.000000:0.000000
A:@0.474152:0.711731:0.485422:0.711731:0.485422:0.695262:0.474152:0.695262:0.000000
:@0.477236:0.709591:0.483652:0.709591:0.483652:0.693773:0.477236:0.693773:0.000000
:@0.489575:0.711097:0.504227:0.711097:0.504227:0.697723:0.489575:0.697723:0.000000
:@0.509021:0.710528:0.522326:0.710528:0.522326:0.697666:0.509021:0.697666:0.000000
2:@0.522326:0.705262:0.527279:0.705262:0.527279:0.695644:0.522326:0.695644:0.000000
S:@0.544695:0.711731:0.552574:0.711731:0.552574:0.695262:0.544695:0.695262:0.000000
:@0.557365:0.711248:0.572715:0.711248:0.572715:0.697238:0.557365:0.697238:0.000000
:@0.577510:0.710528:0.590814:0.710528:0.590814:0.697666:0.577510:0.697666:0.000000
2:@0.590814:0.705262:0.595768:0.705262:0.595768:0.695644:0.590814:0.695644:0.000000
con   ≠ Ø. Se dice que   es ortogonal al conjunto   que se escribe :@0.131975:0.728966:0.599847:0.728966:0.599847:0.712468:0.131975:0.712468:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.162799:0.729082:0.170678:0.729082:0.170678:0.712613:0.162799:0.712613:0.000000
A:@0.293263:0.729082:0.304533:0.729082:0.304533:0.712613:0.293263:0.712613:0.000000
:@0.296384:0.726942:0.302800:0.726942:0.302800:0.711124:0.296384:0.711124:0.000000
S:@0.484719:0.729082:0.492599:0.729082:0.492599:0.712613:0.484719:0.712613:0.000000
A:@0.131975:0.746433:0.143245:0.746433:0.143245:0.729964:0.131975:0.729964:0.000000
:@0.135057:0.744293:0.141472:0.744293:0.141472:0.728475:0.135057:0.728475:0.000000
     si y solo si   ·   = 0    :@0.142628:0.746317:0.329212:0.746317:0.329212:0.729819:0.142628:0.729819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.146770:0.745348:0.162818:0.745348:0.162818:0.731901:0.146770:0.731901:0.000000
S:@0.166960:0.746433:0.174840:0.746433:0.174840:0.729964:0.166960:0.729964:0.000000
A B:@0.253055:0.746433:0.283939:0.746433:0.283939:0.729964:0.253055:0.729964:0.000000:0.000000:0.000000
 :@0.256139:0.744293:0.283130:0.744293:0.283130:0.728475:0.256139:0.728475:0.000000:0.000000:0.000000
∀:@0.329209:0.753903:0.340781:0.753903:0.340781:0.734904:0.329209:0.734904:0.000000
B:@0.340790:0.746433:0.349979:0.746433:0.349979:0.729964:0.340790:0.729964:0.000000
:@0.342755:0.744293:0.349170:0.744293:0.349170:0.728475:0.342755:0.728475:0.000000
    .:@0.351097:0.746317:0.384667:0.746317:0.384667:0.729819:0.351097:0.729819:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.355239:0.745798:0.369891:0.745798:0.369891:0.732425:0.355239:0.732425:0.000000
S:@0.374032:0.746433:0.381912:0.746433:0.381912:0.729964:0.374032:0.729964:0.000000
ii):@0.108230:0.775958:0.123025:0.775958:0.123025:0.759243:0.108230:0.759243:0.000000:0.000000:0.000000
  Sean  ,   dos subconjuntos no vacíos de  . Se dice que   es orto-:@0.123025:0.775740:0.595759:0.775738:0.595759:0.759240:0.123025:0.759243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R S:@0.169378:0.775856:0.193344:0.775856:0.193344:0.759387:0.169378:0.759387:0.000000:0.000000:0.000000
:@0.419084:0.774651:0.432389:0.774651:0.432389:0.761789:0.419084:0.761789:0.000000
2:@0.432389:0.769385:0.437342:0.769385:0.437342:0.759767:0.432389:0.759767:0.000000
R:@0.527830:0.775853:0.537404:0.775853:0.537404:0.759385:0.527830:0.759385:0.000000
gonal a   que se escribe :@0.131967:0.793088:0.302942:0.793088:0.302942:0.776591:0.131967:0.776591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.187008:0.793204:0.194887:0.793204:0.194887:0.776735:0.187008:0.776735:0.000000
R :@0.302942:0.793204:0.316659:0.793204:0.316659:0.776735:0.302942:0.776735:0.000000:0.000000
:@0.316659:0.792120:0.332707:0.792120:0.332707:0.778673:0.316659:0.778673:0.000000
   si y solo si:@0.332707:0.793088:0.418802:0.793088:0.418802:0.776591:0.332707:0.776591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.336849:0.793204:0.344729:0.793204:0.344729:0.776735:0.336849:0.776735:0.000000
 :@0.108233:0.810439:0.112375:0.810439:0.112375:0.793942:0.108233:0.793942:0.000000
A B:@0.131968:0.810555:0.162850:0.810555:0.162850:0.794086:0.131968:0.794086:0.000000:0.000000:0.000000
 :@0.135050:0.808415:0.162041:0.808415:0.162041:0.792597:0.135050:0.792597:0.000000:0.000000:0.000000
 ·   = 0    :@0.142622:0.810439:0.208123:0.810439:0.208123:0.793942:0.142622:0.793942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.208131:0.818026:0.219703:0.818026:0.219703:0.799027:0.208131:0.799027:0.000000
A:@0.219710:0.810555:0.230980:0.810555:0.230980:0.794086:0.219710:0.794086:0.000000
:@0.222793:0.808415:0.229208:0.808415:0.229208:0.792597:0.222793:0.792597:0.000000
    , :@0.230364:0.810439:0.273502:0.810439:0.273502:0.793942:0.230364:0.793942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.234506:0.809921:0.249158:0.809921:0.249158:0.796547:0.234506:0.796547:0.000000
:@0.253300:0.809352:0.266605:0.809352:0.266605:0.796490:0.253300:0.796490:0.000000
∀:@0.273500:0.818026:0.285073:0.818026:0.285073:0.799027:0.273500:0.799027:0.000000
B:@0.285081:0.810555:0.294271:0.810555:0.294271:0.794086:0.285081:0.794086:0.000000
:@0.287046:0.808415:0.293462:0.808415:0.293462:0.792597:0.287046:0.792597:0.000000
    .:@0.295388:0.810439:0.328958:0.810439:0.328958:0.793942:0.295388:0.793942:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.299530:0.809921:0.314183:0.809921:0.314183:0.796547:0.299530:0.796547:0.000000
S:@0.318324:0.810555:0.326204:0.810555:0.326204:0.794086:0.318324:0.794086:0.000000
iii):@0.108236:0.840080:0.127290:0.840080:0.127290:0.823366:0.108236:0.823366:0.000000:0.000000:0.000000:0.000000
 Sea       con   ≠ Ø. Se dice que   es un conjunto ortogonal si        :@0.127291:0.839863:0.599914:0.839860:0.599914:0.823362:0.127291:0.823365:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.160908:0.839978:0.168787:0.839978:0.168787:0.823510:0.160908:0.823510:0.000000
:@0.173608:0.839492:0.188958:0.839492:0.188958:0.825482:0.173608:0.825482:0.000000
:@0.193774:0.838773:0.207079:0.838773:0.207079:0.825911:0.193774:0.825911:0.000000
2:@0.207079:0.833507:0.212032:0.833507:0.212032:0.823889:0.207079:0.823889:0.000000
S:@0.248616:0.839976:0.256495:0.839976:0.256495:0.823507:0.248616:0.823507:0.000000
S:@0.384742:0.839976:0.392621:0.839976:0.392621:0.823507:0.384742:0.823507:0.000000
con   ·   = 0    :@0.131984:0.857211:0.239233:0.857211:0.239233:0.840713:0.131984:0.840713:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.163078:0.857327:0.193960:0.857327:0.193960:0.840858:0.163078:0.840858:0.000000:0.000000:0.000000
 :@0.166160:0.855187:0.193151:0.855187:0.193151:0.839368:0.166160:0.839368:0.000000:0.000000:0.000000
∀:@0.239223:0.864797:0.250796:0.864797:0.250796:0.845798:0.239223:0.845798:0.000000
A, B:@0.250804:0.857327:0.277641:0.857327:0.277641:0.840858:0.250804:0.840858:0.000000:0.000000:0.000000:0.000000
 :@0.253887:0.855187:0.276832:0.855187:0.276832:0.839368:0.253887:0.839368:0.000000:0.000000:0.000000
     con   ≠  .:@0.278758:0.857211:0.387617:0.857211:0.387617:0.840713:0.278758:0.840713:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.282899:0.856692:0.297551:0.856692:0.297551:0.843319:0.282899:0.843319:0.000000
S:@0.301694:0.857327:0.309573:0.857327:0.309573:0.840858:0.301694:0.840858:0.000000
A B:@0.344810:0.857327:0.383745:0.857327:0.383745:0.840858:0.344810:0.840858:0.000000:0.000000:0.000000
:@0.347892:0.855187:0.354307:0.855187:0.354307:0.839368:0.347892:0.839368:0.000000
:@0.376520:0.855187:0.382936:0.855187:0.382936:0.839368:0.376520:0.839368:0.000000
iv):@0.108232:0.886852:0.127035:0.886852:0.127035:0.870137:0.108232:0.870137:0.000000:0.000000:0.000000
 Sea       con   ≠ Ø. El complemento ortogonal de   se nota con :@0.127034:0.886634:0.599915:0.886632:0.599915:0.870134:0.127034:0.870137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.159573:0.886750:0.167453:0.886750:0.167453:0.870281:0.159573:0.870281:0.000000
:@0.170949:0.886264:0.186299:0.886264:0.186299:0.872254:0.170949:0.872254:0.000000
:@0.189785:0.885545:0.203090:0.885545:0.203090:0.872683:0.189785:0.872683:0.000000
2:@0.203090:0.880279:0.208043:0.880279:0.208043:0.870661:0.203090:0.870661:0.000000
S:@0.241970:0.886747:0.249849:0.886747:0.249849:0.870279:0.241970:0.870279:0.000000
S:@0.502550:0.886747:0.510429:0.886747:0.510429:0.870279:0.502550:0.870279:0.000000
S:@0.131985:0.904098:0.139864:0.904098:0.139864:0.887629:0.131985:0.887629:0.000000
:@0.139857:0.897065:0.149212:0.897065:0.149212:0.889225:0.139857:0.889225:0.000000
 y se define como el conjunto.:@0.149211:0.903982:0.362553:0.903982:0.362553:0.887485:0.149211:0.887485:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.228218:0.928577:0.236097:0.928577:0.236097:0.912108:0.228218:0.912108:0.000000
:@0.236107:0.921544:0.245463:0.921544:0.245463:0.913704:0.236107:0.913704:0.000000
 = {      |   ·   = 0,    :@0.245462:0.928461:0.414462:0.928461:0.414462:0.911963:0.245462:0.911963:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.270410:0.928577:0.281681:0.928577:0.281681:0.912108:0.270410:0.912108:0.000000
:@0.273493:0.926437:0.279908:0.926437:0.279908:0.910618:0.273493:0.910618:0.000000
:@0.285205:0.927942:0.299858:0.927942:0.299858:0.914569:0.285205:0.914569:0.000000
:@0.304000:0.927374:0.317305:0.927374:0.317305:0.914512:0.304000:0.914512:0.000000
2:@0.317305:0.922108:0.322258:0.922108:0.322258:0.912490:0.317305:0.912490:0.000000
A B:@0.335551:0.928577:0.366434:0.928577:0.366434:0.912108:0.335551:0.912108:0.000000:0.000000:0.000000
 :@0.338634:0.926437:0.365624:0.926437:0.365624:0.910618:0.338634:0.910618:0.000000:0.000000:0.000000
∀:@0.414458:0.936047:0.426031:0.936047:0.426031:0.917048:0.414458:0.917048:0.000000
B:@0.426039:0.928577:0.435229:0.928577:0.435229:0.912108:0.426039:0.912108:0.000000
:@0.428004:0.926437:0.434420:0.926437:0.434420:0.910618:0.428004:0.910618:0.000000
    }.:@0.436346:0.928461:0.475773:0.928461:0.475773:0.911963:0.436346:0.911963:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.440488:0.927942:0.455141:0.927942:0.455141:0.914569:0.440488:0.914569:0.000000
S:@0.459282:0.928577:0.467162:0.928577:0.467162:0.912108:0.459282:0.912108:0.000000
Competencia digital:@0.684804:0.691434:0.827156:0.691434:0.827156:0.675962:0.684804:0.675962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para conocer más sobre :@0.685042:0.720062:0.843262:0.720062:0.843262:0.704999:0.685042:0.704999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
distancia entre dos puntos en :@0.638498:0.735904:0.833728:0.735904:0.833728:0.720841:0.638498:0.720841:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.638503:0.750743:0.650599:0.750743:0.650599:0.739050:0.638503:0.739050:0.000000
2:@0.650599:0.745946:0.655121:0.745946:0.655121:0.737165:0.650599:0.737165:0.000000
, :@0.655120:0.751746:0.661417:0.751746:0.661417:0.736683:0.655120:0.736683:0.000000:0.000000
visita:@0.661417:0.752168:0.698601:0.752168:0.698601:0.736696:0.661417:0.736696:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 este portal::@0.698603:0.751746:0.774080:0.751746:0.774080:0.736683:0.698603:0.736683:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lynk.ec/12m05:@0.638498:0.775047:0.736386:0.775047:0.736386:0.759733:0.638498:0.759733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.629149:0.592327:0.640629:0.592327:0.640629:0.582303:0.629149:0.582303:0.000000
 :@0.640629:0.593035:0.643511:0.593035:0.643511:0.581558:0.640629:0.581558:0.000000
Figura 2.9.:@0.643511:0.593035:0.692079:0.593035:0.692079:0.581558:0.643511:0.581558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.720046:0.460528:0.725956:0.460528:0.725956:0.449051:0.720046:0.449051:0.000000
–1:@0.712742:0.517549:0.725956:0.517549:0.725956:0.506072:0.712742:0.506072:0.000000:0.000000
–2:@0.712742:0.546065:0.725956:0.546065:0.725956:0.534588:0.712742:0.534588:0.000000:0.000000
–3:@0.712742:0.574580:0.725956:0.574580:0.725956:0.563104:0.712742:0.563104:0.000000:0.000000
2:@0.720046:0.432022:0.725956:0.432022:0.725956:0.420546:0.720046:0.420546:0.000000
1:@0.767958:0.498951:0.773868:0.498951:0.773868:0.487474:0.767958:0.487474:0.000000
–1:@0.688323:0.498951:0.701538:0.498951:0.701538:0.487474:0.688323:0.487474:0.000000:0.000000
–2:@0.653224:0.498951:0.666438:0.498951:0.666438:0.487474:0.653224:0.487474:0.000000:0.000000
2:@0.805939:0.498951:0.811849:0.498951:0.811849:0.487474:0.805939:0.487474:0.000000
0:@0.721473:0.498404:0.728491:0.498404:0.728491:0.484775:0.721473:0.484775:0.000000
y:@0.718752:0.415426:0.725213:0.415426:0.725213:0.401798:0.718752:0.401798:0.000000
x:@0.838940:0.499670:0.845545:0.499670:0.845545:0.486041:0.838940:0.486041:0.000000
A:@0.641871:0.460991:0.651671:0.460991:0.651671:0.446670:0.641871:0.446670:0.000000
:@0.644551:0.459017:0.650130:0.459017:0.650130:0.445262:0.644551:0.445262:0.000000
B:@0.779642:0.432198:0.787633:0.432198:0.787633:0.417878:0.779642:0.417878:0.000000
:@0.781770:0.430225:0.787348:0.430225:0.787348:0.416470:0.781770:0.416470:0.000000
C:@0.817436:0.576511:0.826164:0.576511:0.826164:0.562191:0.817436:0.562191:0.000000
:@0.821138:0.574538:0.826717:0.574538:0.826717:0.560783:0.821138:0.560783:0.000000
Competencia :@0.685338:0.100040:0.782961:0.100040:0.782961:0.084568:0.685338:0.084568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.685338:0.112608:0.769401:0.112608:0.769401:0.097136:0.685338:0.097136:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Teorema:@0.685576:0.137504:0.746699:0.137504:0.746699:0.122032:0.685576:0.122032:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,  ,   :@0.639033:0.152924:0.717135:0.152924:0.717135:0.137861:0.639033:0.137861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B C:@0.673549:0.153029:0.712772:0.153029:0.712772:0.137993:0.673549:0.137993:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.676364:0.151075:0.713353:0.151075:0.713353:0.136633:0.676364:0.136633:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.717134:0.152575:0.731089:0.152575:0.731089:0.139838:0.717134:0.139838:0.000000
 :@0.731089:0.152726:0.735486:0.152726:0.735486:0.139352:0.731089:0.139352:0.000000
:@0.735486:0.151921:0.747582:0.151921:0.747582:0.140228:0.735486:0.140228:0.000000
2:@0.747582:0.147124:0.752104:0.147124:0.752104:0.138343:0.747582:0.138343:0.000000
.:@0.752105:0.152924:0.754620:0.152924:0.754620:0.137861:0.752105:0.137861:0.000000
La distancia entre dos puntos :@0.639036:0.168766:0.833052:0.168766:0.833052:0.153703:0.639036:0.153703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de  , cumple las propiedades :@0.639036:0.184608:0.839836:0.184608:0.839836:0.169545:0.639036:0.169545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.659126:0.183605:0.671221:0.183605:0.671221:0.171912:0.659126:0.171912:0.000000
2:@0.671221:0.178808:0.675743:0.178808:0.675743:0.170027:0.671221:0.170027:0.000000
siguientes::@0.639032:0.200450:0.705100:0.200450:0.705100:0.185387:0.639032:0.185387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i):@0.639032:0.223619:0.648654:0.223619:0.648654:0.208357:0.639032:0.208357:0.000000:0.000000
     ( ,  ) ≥ 0.:@0.648654:0.223420:0.733932:0.223420:0.733932:0.208357:0.648654:0.208357:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d A B:@0.663218:0.223526:0.701093:0.223526:0.701093:0.208490:0.663218:0.208489:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.679845:0.221572:0.700793:0.221572:0.700793:0.207130:0.679845:0.207130:0.000000:0.000000:0.000000
ii):@0.639034:0.243025:0.652543:0.243025:0.652543:0.227764:0.639034:0.227764:0.000000:0.000000:0.000000
    ( ,  ) = 0     =  .:@0.652544:0.242827:0.792244:0.242826:0.792244:0.227763:0.652544:0.227764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d A B:@0.663220:0.242933:0.701093:0.242931:0.701093:0.227895:0.663220:0.227896:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.679845:0.240977:0.700793:0.240977:0.700793:0.226535:0.679845:0.226535:0.000000:0.000000:0.000000
A B:@0.754832:0.242931:0.790028:0.242931:0.790028:0.227895:0.754832:0.227895:0.000000:0.000000:0.000000
:@0.757646:0.240977:0.763504:0.240977:0.763504:0.226535:0.757646:0.226535:0.000000
:@0.783871:0.240977:0.789729:0.240977:0.789729:0.226535:0.783871:0.226535:0.000000
iii):@0.639035:0.262430:0.654849:0.262430:0.654849:0.247169:0.639035:0.247169:0.000000:0.000000:0.000000:0.000000
    ( ,  ) =  ( ,  ).:@0.654321:0.262232:0.770060:0.262232:0.770060:0.247169:0.654321:0.247169:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d A B:@0.663222:0.262338:0.701093:0.262338:0.701093:0.247302:0.663222:0.247301:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.679845:0.260384:0.700793:0.260384:0.700793:0.245942:0.679845:0.245942:0.000000:0.000000:0.000000
d B A:@0.723659:0.262338:0.763024:0.262338:0.763024:0.247302:0.723659:0.247301:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.739700:0.260384:0.761406:0.260384:0.761406:0.245942:0.739700:0.245942:0.000000:0.000000:0.000000
iv):@0.639032:0.281837:0.654793:0.281837:0.654793:0.266575:0.639032:0.266575:0.000000:0.000000:0.000000
    ( ,  ) ≤  ( ,  ) +  ( ,  ):@0.654088:0.281639:0.829652:0.281637:0.829652:0.266574:0.654088:0.266575:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d A B:@0.663218:0.281744:0.701093:0.281743:0.701093:0.266707:0.663218:0.266707:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.679845:0.279789:0.700793:0.279789:0.700793:0.265347:0.679845:0.265347:0.000000:0.000000:0.000000
d A C:@0.723659:0.281743:0.762302:0.281743:0.762302:0.266707:0.723659:0.266706:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.740281:0.279789:0.762883:0.279789:0.762883:0.265347:0.740281:0.265347:0.000000:0.000000:0.000000
d C B:@0.786278:0.281743:0.824516:0.281743:0.824516:0.266707:0.786278:0.266706:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.803972:0.279789:0.824217:0.279789:0.824217:0.265347:0.803972:0.265347:0.000000:0.000000:0.000000
    (desigualdad triangular). :@0.639046:0.297479:0.823478:0.297479:0.823478:0.282416:0.639046:0.282416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El espacio  , provisto de la :@0.639047:0.320450:0.820243:0.320450:0.820243:0.305387:0.639047:0.305387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.706213:0.319447:0.718308:0.319447:0.718308:0.307755:0.706213:0.307755:0.000000
2:@0.718308:0.314650:0.722831:0.314650:0.722831:0.305868:0.718308:0.305868:0.000000
métrica o distancia  , se llama :@0.639031:0.336292:0.835932:0.336292:0.835932:0.321229:0.639031:0.321229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.765695:0.336398:0.774068:0.336398:0.774068:0.321361:0.765695:0.321361:0.000000
espacio métrico y se escribe :@0.639031:0.352134:0.823213:0.352134:0.823213:0.337071:0.639031:0.337071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ).:@0.639031:0.367976:0.683711:0.367976:0.683711:0.352913:0.639031:0.352913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.644472:0.366973:0.656567:0.366973:0.656567:0.355281:0.644472:0.355281:0.000000
2:@0.656567:0.362175:0.661090:0.362175:0.661090:0.353394:0.656567:0.353394:0.000000
d:@0.667388:0.368082:0.675761:0.368082:0.675761:0.353045:0.667388:0.353045:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000