75:@0.922460:0.966765:0.939432:0.966765:0.939432:0.950778:0.922460:0.950778:0.000000:0.000000
Igualdad de vectores:@0.108233:0.097328:0.273776:0.097328:0.273776:0.079645:0.108233:0.079645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.108233:0.121627:0.188317:0.121627:0.188317:0.104681:0.108233:0.104681:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.108233:0.139137:0.146031:0.139137:0.146031:0.122639:0.108233:0.122639:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.150137:0.140517:0.170520:0.140517:0.170520:0.124048:0.150137:0.124048:0.000000:0.000000
 y :@0.173224:0.139144:0.189715:0.139144:0.189715:0.122646:0.173224:0.122646:0.000000:0.000000:0.000000
CD:@0.192672:0.140517:0.214307:0.140517:0.214307:0.124048:0.192672:0.124048:0.000000:0.000000
 dos vectores asociados a los bipuntos (:@0.216909:0.139144:0.500640:0.139144:0.500640:0.122646:0.216909:0.122646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A, B:@0.500640:0.139259:0.528864:0.139259:0.528864:0.122791:0.500640:0.122791:0.000000:0.000000:0.000000:0.000000
) y (:@0.528864:0.139144:0.557646:0.139144:0.557646:0.122646:0.528864:0.122646:0.000000:0.000000:0.000000:0.000000:0.000000
C, D:@0.557646:0.139259:0.587026:0.139259:0.587026:0.122791:0.557646:0.122791:0.000000:0.000000:0.000000:0.000000
). :@0.587026:0.139144:0.599876:0.139144:0.599876:0.122646:0.587026:0.122646:0.000000:0.000000:0.000000
Decimos que :@0.108234:0.157116:0.207236:0.157116:0.207236:0.140618:0.108234:0.140618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.211572:0.158496:0.231955:0.158496:0.231955:0.142027:0.211572:0.142027:0.000000:0.000000
 y :@0.234660:0.157123:0.251382:0.157123:0.251382:0.140625:0.234660:0.140625:0.000000:0.000000:0.000000
CD:@0.254567:0.158496:0.276202:0.158496:0.276202:0.142027:0.254567:0.142027:0.000000:0.000000
 son iguales, o sea que :@0.278806:0.157123:0.441902:0.157123:0.441902:0.140625:0.278806:0.140625:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.446248:0.158496:0.466630:0.158496:0.466630:0.142027:0.446248:0.142027:0.000000:0.000000
 = :@0.469334:0.157123:0.489043:0.157123:0.489043:0.140625:0.469334:0.140625:0.000000:0.000000:0.000000
CD:@0.492228:0.158496:0.513863:0.158496:0.513863:0.142027:0.492228:0.142027:0.000000:0.000000
, si y solo si :@0.516466:0.157123:0.599901:0.157123:0.599901:0.140625:0.516466:0.140625:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los segmentos de recta [:@0.108235:0.174474:0.284084:0.174474:0.284084:0.157976:0.108235:0.157976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A, B:@0.284084:0.174589:0.312674:0.174589:0.312674:0.158121:0.284084:0.158121:0.000000:0.000000:0.000000:0.000000
] y [:@0.312674:0.174474:0.341995:0.174474:0.341995:0.157976:0.312674:0.157976:0.000000:0.000000:0.000000:0.000000:0.000000
C, D:@0.341995:0.174589:0.371741:0.174589:0.371741:0.158121:0.341995:0.158121:0.000000:0.000000:0.000000:0.000000
] tienen exactamente el mismo :@0.371741:0.174474:0.599820:0.174474:0.599820:0.157976:0.371741:0.157976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
punto medio.:@0.108235:0.191825:0.205447:0.191825:0.205447:0.175327:0.108235:0.175327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En la figura 2.2. se muestran dos vectores iguales :@0.108235:0.218718:0.463328:0.218718:0.463328:0.202221:0.108235:0.202221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.468252:0.220086:0.488635:0.220086:0.488635:0.203617:0.468252:0.203617:0.000000:0.000000
 = :@0.491340:0.218713:0.511704:0.218713:0.511704:0.202215:0.491340:0.202215:0.000000:0.000000:0.000000
CD:@0.515526:0.220086:0.537161:0.220086:0.537161:0.203617:0.515526:0.203617:0.000000:0.000000
, y en la :@0.539765:0.218713:0.599930:0.218713:0.599930:0.202215:0.539765:0.202215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
figura 2.3. se muestran los vectores :@0.108242:0.236686:0.353660:0.236686:0.353660:0.220188:0.108242:0.220188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.356576:0.238066:0.376958:0.238066:0.376958:0.221597:0.356576:0.221597:0.000000:0.000000
 y :@0.379662:0.236693:0.394939:0.236693:0.394939:0.220195:0.379662:0.220195:0.000000:0.000000:0.000000
CD:@0.396689:0.238066:0.418324:0.238066:0.418324:0.221597:0.396689:0.221597:0.000000:0.000000
 y los segmentos de recta  :@0.420927:0.236693:0.599901:0.236693:0.599901:0.220195:0.420927:0.220195:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.108232:0.254043:0.114089:0.254043:0.114089:0.237546:0.108232:0.237546:0.000000
A, D:@0.114089:0.254159:0.144374:0.254159:0.144374:0.237690:0.114089:0.237690:0.000000:0.000000:0.000000:0.000000
] y [:@0.144374:0.254043:0.172193:0.254043:0.172193:0.237546:0.144374:0.237546:0.000000:0.000000:0.000000:0.000000:0.000000
B, C:@0.172193:0.254159:0.198278:0.254159:0.198278:0.237690:0.172193:0.237690:0.000000:0.000000:0.000000:0.000000
] que se intersectan en el punto  .:@0.198278:0.254043:0.434293:0.254043:0.434293:0.237546:0.198278:0.237546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
I:@0.427531:0.254159:0.431538:0.254159:0.431538:0.237690:0.427531:0.237690:0.000000
Sean :@0.108232:0.280301:0.146031:0.280301:0.146031:0.263803:0.108232:0.263803:0.000000:0.000000:0.000000:0.000000:0.000000
A, B, C, D :@0.145742:0.280416:0.212698:0.280416:0.212698:0.263948:0.145742:0.263948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuatro puntos del plano tales que los bipuntos (:@0.212409:0.280301:0.550678:0.280301:0.550678:0.263803:0.212409:0.263803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A, B:@0.550678:0.280416:0.578227:0.280416:0.578227:0.263948:0.550678:0.263948:0.000000:0.000000:0.000000:0.000000
) y :@0.578227:0.280301:0.599997:0.280301:0.599997:0.263803:0.578227:0.263803:0.000000:0.000000:0.000000:0.000000
(:@0.108232:0.298273:0.114185:0.298273:0.114185:0.281776:0.108232:0.281776:0.000000
C, D:@0.114185:0.298389:0.143179:0.298389:0.143179:0.281920:0.114185:0.281920:0.000000:0.000000:0.000000:0.000000
) son representantes de los vectores :@0.143179:0.298273:0.401330:0.298273:0.401330:0.281776:0.143179:0.281776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.405045:0.299657:0.425428:0.299657:0.425428:0.283188:0.405045:0.283188:0.000000:0.000000
 y :@0.428132:0.298284:0.444238:0.298284:0.444238:0.281786:0.428132:0.281786:0.000000:0.000000:0.000000
CD:@0.446804:0.299657:0.468439:0.299657:0.468439:0.283188:0.446804:0.283188:0.000000:0.000000
.:@0.471041:0.298284:0.473796:0.298284:0.473796:0.281786:0.471041:0.281786:0.000000
En la figura 2.4. la igualdad :@0.108238:0.325178:0.304089:0.325178:0.304089:0.308680:0.108238:0.308680:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.309114:0.326547:0.329497:0.326547:0.329497:0.310078:0.309114:0.310078:0.000000:0.000000
 = :@0.332201:0.325174:0.352584:0.325174:0.352584:0.308676:0.332201:0.308676:0.000000:0.000000:0.000000
CD:@0.356448:0.326547:0.378083:0.326547:0.378083:0.310078:0.356448:0.310078:0.000000:0.000000
 significa que :@0.380687:0.325174:0.479364:0.325174:0.479364:0.308676:0.380687:0.308676:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ABCD:@0.480655:0.325290:0.522653:0.325290:0.522653:0.308821:0.480655:0.308821:0.000000:0.000000:0.000000:0.000000
 es un pa-:@0.522672:0.325174:0.595765:0.325174:0.595765:0.308676:0.522672:0.308676:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ralelogramo. Es decir que los segmentos de recta [:@0.108238:0.342525:0.480320:0.342525:0.480320:0.326027:0.108238:0.326027:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A, B:@0.480320:0.342640:0.510335:0.342640:0.510335:0.326172:0.480320:0.326172:0.000000:0.000000:0.000000:0.000000
] || [:@0.510335:0.342525:0.544704:0.342525:0.544704:0.326027:0.510335:0.326027:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C, D:@0.544704:0.342640:0.575873:0.342640:0.575873:0.326172:0.544704:0.326172:0.000000:0.000000:0.000000:0.000000
] y :@0.575873:0.342525:0.600013:0.342525:0.600013:0.326027:0.575873:0.326027:0.000000:0.000000:0.000000:0.000000
 :@0.595765:0.342525:0.599907:0.342525:0.599907:0.326027:0.595765:0.326027:0.000000
[:@0.108238:0.359875:0.114095:0.359875:0.114095:0.343378:0.108238:0.343378:0.000000
A, C:@0.114095:0.359991:0.144900:0.359991:0.144900:0.343522:0.114095:0.343522:0.000000:0.000000:0.000000:0.000000
] || [:@0.144900:0.359875:0.179153:0.359875:0.179153:0.343378:0.144900:0.343378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B, D:@0.179153:0.359991:0.208957:0.359991:0.208957:0.343522:0.179153:0.343522:0.000000:0.000000:0.000000:0.000000
] y las longitudes de los segmentos de recta [:@0.208976:0.359875:0.545843:0.359875:0.545843:0.343378:0.208976:0.343378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A, B:@0.545843:0.359991:0.575800:0.359991:0.575800:0.343522:0.545843:0.343522:0.000000:0.000000:0.000000:0.000000
] y  :@0.575800:0.359875:0.599926:0.359875:0.599926:0.343378:0.575800:0.343378:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.108257:0.377226:0.114114:0.377226:0.114114:0.360728:0.108257:0.360728:0.000000
C, D:@0.114114:0.377342:0.144900:0.377342:0.144900:0.360873:0.114114:0.360873:0.000000:0.000000:0.000000:0.000000
] son iguales. De modo similar [:@0.144900:0.377226:0.379179:0.377226:0.379179:0.360728:0.144900:0.360728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A, C:@0.379179:0.377342:0.409657:0.377342:0.409657:0.360873:0.379179:0.360873:0.000000:0.000000:0.000000:0.000000
] y [:@0.409657:0.377226:0.441059:0.377226:0.441059:0.360728:0.409657:0.360728:0.000000:0.000000:0.000000:0.000000:0.000000
B, D:@0.441059:0.377342:0.470535:0.377342:0.470535:0.360873:0.441059:0.360873:0.000000:0.000000:0.000000:0.000000
] son iguales y se :@0.470540:0.377226:0.599924:0.377226:0.599924:0.360728:0.470540:0.360728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
intersectan en el punto  .:@0.108257:0.394577:0.284417:0.394577:0.284417:0.378079:0.108257:0.378079:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
I:@0.277655:0.394693:0.281662:0.394693:0.281662:0.378224:0.277655:0.378224:0.000000
Sean :@0.108257:0.420834:0.146056:0.420834:0.146056:0.404337:0.108257:0.404337:0.000000:0.000000:0.000000:0.000000:0.000000
A, B, C, D:@0.146037:0.420950:0.209670:0.420950:0.209670:0.404481:0.146037:0.404481:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 cuatro puntos del plano tales que :@0.209670:0.420834:0.456436:0.420834:0.456436:0.404337:0.209670:0.404337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A ≠ B, C ≠ D:@0.456417:0.420950:0.543650:0.420950:0.543650:0.404481:0.456417:0.404481:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Deno-:@0.543650:0.420834:0.595784:0.420834:0.595784:0.404337:0.543650:0.404337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tamos con   el soporte del bipunto (:@0.108257:0.438185:0.374811:0.438188:0.374811:0.421690:0.108257:0.421687:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.186773:0.438301:0.194614:0.438301:0.194614:0.421832:0.186773:0.421832:0.000000
AB:@0.194583:0.440860:0.205751:0.440860:0.205751:0.432078:0.194583:0.432078:0.000000:0.000000
A, B:@0.374811:0.438303:0.401850:0.438303:0.401850:0.421835:0.374811:0.421835:0.000000:0.000000:0.000000:0.000000
), y con :@0.401850:0.438188:0.456178:0.438188:0.456178:0.421690:0.401850:0.421690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.455332:0.438303:0.463173:0.438303:0.463173:0.421835:0.455332:0.421835:0.000000
CD:@0.463173:0.440860:0.475663:0.440860:0.475663:0.432078:0.463173:0.432078:0.000000:0.000000
 la recta que pasa :@0.475663:0.438188:0.599940:0.438188:0.599940:0.421690:0.475663:0.421690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por los puntos   y   que es el soporte del bipunto (:@0.108236:0.455538:0.475272:0.455538:0.475272:0.439041:0.108236:0.439041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C D:@0.215852:0.455654:0.253400:0.455654:0.253400:0.439185:0.215852:0.439185:0.000000:0.000000:0.000000
C, D:@0.475272:0.455654:0.504151:0.455654:0.504151:0.439185:0.475272:0.439185:0.000000:0.000000:0.000000:0.000000
) (figura 2.5.).:@0.504151:0.455538:0.595697:0.455538:0.595697:0.439041:0.504151:0.439041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Se designa con [:@0.108236:0.481796:0.228452:0.481796:0.228452:0.465298:0.108236:0.465298:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A, B:@0.228452:0.481912:0.258005:0.481912:0.258005:0.465443:0.228452:0.465443:0.000000:0.000000:0.000000:0.000000
[ la semirrecta que tiene como punto inicial u :@0.258005:0.481796:0.599901:0.481796:0.599901:0.465298:0.258005:0.465298:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
origen   y que pasa por  . De modo similar, [:@0.108236:0.499147:0.428094:0.499147:0.428094:0.482649:0.108236:0.482649:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.157093:0.499262:0.168363:0.499262:0.168363:0.482794:0.157093:0.482794:0.000000
B:@0.281391:0.499262:0.290580:0.499262:0.290580:0.482794:0.281391:0.482794:0.000000
C, D:@0.428094:0.499262:0.457088:0.499262:0.457088:0.482794:0.428094:0.482794:0.000000:0.000000:0.000000:0.000000
[ (figura 2.6.).:@0.457088:0.499147:0.548771:0.499147:0.548771:0.482649:0.457088:0.482649:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Propiedades:@0.108236:0.548567:0.203482:0.548567:0.203482:0.531621:0.108236:0.531621:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para que haya igualdad de los vectores :@0.108236:0.573205:0.386558:0.573205:0.386558:0.556708:0.108236:0.556708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.390469:0.574588:0.410852:0.574588:0.410852:0.558120:0.390469:0.558120:0.000000:0.000000
 y :@0.413556:0.573215:0.429892:0.573215:0.429892:0.556718:0.413556:0.556718:0.000000:0.000000:0.000000
CD:@0.432680:0.574588:0.454315:0.574588:0.454315:0.558120:0.432680:0.558120:0.000000:0.000000
, esto es, :@0.456917:0.573215:0.519641:0.573215:0.519641:0.556718:0.456917:0.556718:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.523577:0.574588:0.543960:0.574588:0.543960:0.558120:0.523577:0.558120:0.000000:0.000000
 = :@0.546665:0.573215:0.565988:0.573215:0.565988:0.556718:0.546665:0.556718:0.000000:0.000000:0.000000
CD:@0.568775:0.574588:0.590410:0.574588:0.590410:0.558120:0.568775:0.558120:0.000000:0.000000
, :@0.593012:0.573215:0.599909:0.573215:0.599909:0.556718:0.593012:0.556718:0.000000:0.000000
deben verificarse las tres propiedades siguientes::@0.108241:0.590566:0.449116:0.590566:0.449116:0.574069:0.108241:0.574069:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.108241:0.617041:0.120513:0.617041:0.120513:0.600326:0.108241:0.600326:0.000000:0.000000
 :@0.120513:0.616824:0.124655:0.616824:0.124655:0.600326:0.120513:0.600326:0.000000
L:@0.131976:0.616939:0.139817:0.616939:0.139817:0.600471:0.131976:0.600471:0.000000
AB:@0.139818:0.619499:0.150986:0.619499:0.150986:0.610717:0.139818:0.610717:0.000000:0.000000
 || :@0.150985:0.616826:0.169287:0.616826:0.169287:0.600329:0.150985:0.600329:0.000000:0.000000:0.000000:0.000000
L:@0.169287:0.616942:0.177128:0.616942:0.177128:0.600473:0.169287:0.600473:0.000000
CD:@0.177127:0.619499:0.189618:0.619499:0.189618:0.610717:0.177127:0.610717:0.000000:0.000000
, y   y :@0.189618:0.616826:0.243592:0.616826:0.243592:0.600329:0.189618:0.600329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.208479:0.616942:0.216320:0.616942:0.216320:0.600473:0.208479:0.600473:0.000000
AB:@0.216320:0.619499:0.227487:0.619499:0.227487:0.610717:0.216320:0.610717:0.000000:0.000000
L:@0.243592:0.616942:0.251433:0.616942:0.251433:0.600473:0.243592:0.600473:0.000000
CD:@0.251433:0.619499:0.263923:0.619499:0.263923:0.610717:0.251433:0.610717:0.000000:0.000000
 tienen la misma dirección.:@0.263923:0.616826:0.452875:0.616826:0.452875:0.600329:0.263923:0.600329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.:@0.108241:0.643301:0.120513:0.643301:0.120513:0.626586:0.108241:0.626586:0.000000:0.000000
  Las semirrectas [:@0.120513:0.643084:0.249820:0.643084:0.249820:0.626586:0.120513:0.626586:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A, B:@0.249820:0.643199:0.277656:0.643199:0.277656:0.626731:0.249820:0.626731:0.000000:0.000000:0.000000:0.000000
[ y [:@0.277656:0.643084:0.305475:0.643084:0.305475:0.626586:0.277656:0.626586:0.000000:0.000000:0.000000:0.000000:0.000000
C, D:@0.305475:0.643199:0.334468:0.643199:0.334468:0.626731:0.305475:0.626731:0.000000:0.000000:0.000000:0.000000
[ tienen el mismo sentido.:@0.334468:0.643084:0.518389:0.643084:0.518389:0.626586:0.334468:0.626586:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.:@0.108241:0.669558:0.120513:0.669558:0.120513:0.652843:0.108241:0.652843:0.000000:0.000000
  Los segmentos [:@0.120513:0.669341:0.248489:0.669341:0.248489:0.652843:0.120513:0.652843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A, B:@0.248512:0.669457:0.277178:0.669457:0.277178:0.652988:0.248512:0.652988:0.000000:0.000000:0.000000:0.000000
] y [:@0.277178:0.669341:0.306654:0.669341:0.306654:0.652843:0.277178:0.652843:0.000000:0.000000:0.000000:0.000000:0.000000
C, D:@0.306654:0.669457:0.336477:0.669457:0.336477:0.652988:0.306654:0.652988:0.000000:0.000000:0.000000:0.000000
] tienen la misma longitud. Además, :@0.336477:0.669341:0.599848:0.669341:0.599848:0.652843:0.336477:0.652843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[A, C] || [B, D].:@0.131976:0.686692:0.235161:0.686692:0.235161:0.670194:0.131976:0.670194:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea  un vector del plano. Existen dos puntos A, B, tales que el bipun-:@0.108241:0.712949:0.595768:0.712959:0.595768:0.696462:0.108241:0.696452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.138103:0.713075:0.147311:0.713075:0.147311:0.696606:0.138103:0.696606:0.000000
to (A, B) es representante del vector :@0.108226:0.730932:0.374526:0.730932:0.374526:0.714434:0.108226:0.714434:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.379196:0.732312:0.399579:0.732312:0.399579:0.715843:0.379196:0.715843:0.000000:0.000000
 y  =:@0.402283:0.730939:0.446229:0.730939:0.446229:0.714441:0.402283:0.714441:0.000000:0.000000:0.000000:0.000000:0.000000
u AB:@0.422490:0.731055:0.470328:0.732312:0.470328:0.715843:0.422490:0.714586:0.000000:0.000000:0.000000:0.000000
. Sea   un punto :@0.473032:0.730939:0.599932:0.730939:0.599932:0.714441:0.473032:0.714441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
O:@0.510156:0.731055:0.522062:0.731055:0.522062:0.714586:0.510156:0.714586:0.000000
del plano. Existe un único punto   del plano, tal que :@0.108225:0.748911:0.482275:0.748911:0.482275:0.732414:0.108225:0.732414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.341930:0.749027:0.351967:0.749027:0.351967:0.732558:0.341930:0.732558:0.000000
AB:@0.486000:0.750291:0.506382:0.750291:0.506382:0.733822:0.486000:0.733822:0.000000:0.000000
= :@0.509086:0.748918:0.524036:0.748918:0.524036:0.732421:0.509086:0.732421:0.000000:0.000000
OC:@0.526601:0.750291:0.548255:0.750291:0.548255:0.733822:0.526601:0.733822:0.000000:0.000000
 =  .:@0.552515:0.748918:0.589440:0.748918:0.589440:0.732421:0.552515:0.732421:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.573754:0.749034:0.582962:0.749034:0.582962:0.732565:0.573754:0.732565:0.000000
En la figura 2.7. se muestran el vector   = :@0.108232:0.775812:0.400308:0.775808:0.400308:0.759310:0.108232:0.759314:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.369113:0.777181:0.378322:0.777181:0.378322:0.760712:0.369113:0.760712:0.000000
AB:@0.403211:0.777181:0.423594:0.777181:0.423594:0.760712:0.403211:0.760712:0.000000:0.000000
, y los puntos   y   tales :@0.426297:0.775808:0.599897:0.775808:0.599897:0.759310:0.426297:0.759310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
O C,:@0.520368:0.775924:0.559939:0.775924:0.559939:0.759455:0.520368:0.759455:0.000000:0.000000:0.000000:0.000000
que :@0.108228:0.793781:0.139378:0.793781:0.139378:0.777283:0.108228:0.777283:0.000000:0.000000:0.000000:0.000000
AB:@0.143101:0.795161:0.163484:0.795161:0.163484:0.778692:0.143101:0.778692:0.000000:0.000000
= :@0.166188:0.793788:0.181138:0.793788:0.181138:0.777290:0.166188:0.777290:0.000000:0.000000
OC:@0.183703:0.795161:0.205357:0.795161:0.205357:0.778692:0.183703:0.778692:0.000000:0.000000
.:@0.209617:0.793788:0.212372:0.793788:0.212372:0.777290:0.209617:0.777290:0.000000
AB:@0.689045:0.153066:0.709428:0.153066:0.709428:0.136597:0.689045:0.136597:0.000000:0.000000
CD:@0.756485:0.153066:0.778120:0.153066:0.778120:0.136597:0.756485:0.136597:0.000000:0.000000
p:@0.793223:0.198239:0.804704:0.198239:0.804704:0.188214:0.793223:0.188214:0.000000
 :@0.804704:0.198947:0.807585:0.198947:0.807585:0.187470:0.804704:0.187470:0.000000
Figura 2.2.:@0.807585:0.198947:0.856154:0.198947:0.856154:0.187470:0.807585:0.187470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.793223:0.380618:0.804704:0.380618:0.804704:0.370593:0.793223:0.370593:0.000000
 Figura 2.3.:@0.804704:0.381326:0.856154:0.381326:0.856154:0.369849:0.804704:0.369849:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.639108:0.321211:0.659491:0.321211:0.659491:0.304742:0.639108:0.304742:0.000000:0.000000
CD:@0.825530:0.321211:0.847165:0.321211:0.847165:0.304742:0.825530:0.304742:0.000000:0.000000
A:@0.644744:0.360872:0.654054:0.360872:0.654054:0.347268:0.644744:0.347268:0.000000
D:@0.830262:0.279663:0.839875:0.279663:0.839875:0.266058:0.830262:0.266058:0.000000
C:@0.817148:0.360872:0.825440:0.360872:0.825440:0.347268:0.817148:0.347268:0.000000
B:@0.657937:0.279663:0.665528:0.279663:0.665528:0.266058:0.657937:0.266058:0.000000
I:@0.744131:0.310312:0.747442:0.310312:0.747442:0.296707:0.744131:0.296707:0.000000
p:@0.793223:0.938448:0.804704:0.938448:0.804704:0.928423:0.793223:0.928423:0.000000
 :@0.804704:0.939155:0.807585:0.939155:0.807585:0.927679:0.804704:0.927679:0.000000
Figura 2.6.:@0.807585:0.939155:0.856154:0.939155:0.856154:0.927679:0.807585:0.927679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.705568:0.863951:0.713160:0.863951:0.713160:0.850347:0.705568:0.850347:0.000000
[:@0.714353:0.839931:0.719191:0.839931:0.719191:0.826303:0.714353:0.826303:0.000000
A, B:@0.719191:0.840027:0.742188:0.840027:0.742188:0.826422:0.719191:0.826422:0.000000:0.000000:0.000000:0.000000
[:@0.742188:0.839931:0.747026:0.839931:0.747026:0.826303:0.742188:0.826303:0.000000
[:@0.773238:0.843491:0.778076:0.843491:0.778076:0.829862:0.773238:0.829862:0.000000
C, D:@0.778076:0.843586:0.802028:0.843586:0.802028:0.829981:0.778076:0.829981:0.000000:0.000000:0.000000:0.000000
[:@0.802028:0.843491:0.806866:0.843491:0.806866:0.829862:0.802028:0.829862:0.000000
D:@0.789089:0.873220:0.798702:0.873220:0.798702:0.859615:0.789089:0.859615:0.000000
C:@0.729440:0.917773:0.737732:0.917773:0.737732:0.904168:0.729440:0.904168:0.000000
A:@0.650583:0.909937:0.659893:0.909937:0.659893:0.896332:0.650583:0.896332:0.000000
p:@0.793223:0.752505:0.804704:0.752505:0.804704:0.742480:0.793223:0.742480:0.000000
 :@0.804704:0.753213:0.807585:0.753213:0.807585:0.741736:0.804704:0.741736:0.000000
Figura 2.5.:@0.807585:0.753213:0.856154:0.753213:0.856154:0.741736:0.807585:0.741736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.747476:0.682789:0.755067:0.682789:0.755067:0.669185:0.747476:0.669185:0.000000
D:@0.793486:0.700610:0.803098:0.700610:0.803098:0.687006:0.793486:0.687006:0.000000
L:@0.767656:0.653872:0.774133:0.653872:0.774133:0.640267:0.767656:0.640267:0.000000
AB:@0.774132:0.657088:0.785300:0.657088:0.785300:0.648306:0.774132:0.648306:0.000000:0.000000
L:@0.811819:0.667732:0.818296:0.667732:0.818296:0.654127:0.811819:0.654127:0.000000
CD:@0.818295:0.670950:0.830786:0.670950:0.830786:0.662168:0.818295:0.662168:0.000000:0.000000
C:@0.715310:0.725558:0.723601:0.725558:0.723601:0.711953:0.715310:0.711953:0.000000
A:@0.660658:0.714867:0.669969:0.714867:0.669969:0.701263:0.660658:0.701263:0.000000
p:@0.793223:0.566561:0.804704:0.566561:0.804704:0.556537:0.793223:0.556537:0.000000
 Figura 2.4.:@0.804704:0.567269:0.856154:0.567269:0.856154:0.555792:0.804704:0.555792:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.677875:0.461477:0.685466:0.461477:0.685466:0.447872:0.677875:0.447872:0.000000
D:@0.812673:0.461477:0.822286:0.461477:0.822286:0.447872:0.812673:0.447872:0.000000
C:@0.798382:0.547369:0.806673:0.547369:0.806673:0.533764:0.798382:0.533764:0.000000
A:@0.663010:0.547380:0.672321:0.547380:0.672321:0.533776:0.663010:0.533776:0.000000
I:@0.742950:0.497830:0.746260:0.497830:0.746260:0.484226:0.742950:0.484226:0.000000
p:@0.426346:0.939705:0.437826:0.939705:0.437826:0.929680:0.426346:0.929680:0.000000
 :@0.437826:0.940413:0.440708:0.940413:0.440708:0.928936:0.437826:0.928936:0.000000
Figura 2.7.:@0.440708:0.940413:0.489276:0.940413:0.489276:0.928936:0.440708:0.928936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.219452:0.886540:0.230624:0.886540:0.230624:0.870214:0.219452:0.870214:0.000000
B:@0.298670:0.816450:0.307779:0.816450:0.307779:0.800124:0.298670:0.800124:0.000000
0:@0.400900:0.920638:0.409322:0.920638:0.409322:0.904284:0.400900:0.904284:0.000000
C:@0.469327:0.827214:0.479277:0.827214:0.479277:0.810889:0.469327:0.810889:0.000000
I:@0.342668:0.872337:0.346640:0.872337:0.346640:0.856012:0.342668:0.856012:0.000000
u:@0.274258:0.862797:0.284203:0.862797:0.284203:0.845011:0.274258:0.845011:0.000000
u:@0.417809:0.885720:0.427755:0.885720:0.427755:0.867934:0.417809:0.867934:0.000000
 ©:@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