152:@0.067867:0.963104:0.109245:0.963104:0.109245:0.941283:0.067867:0.941283:0.000000:0.000000:0.000000
Matemática:@0.120102:0.956142:0.204868:0.956142:0.204868:0.943479:0.120102:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.º BG:@0.120102:0.967458:0.162238:0.967458:0.162238:0.954794:0.120102:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
isposición y compromiso:@0.306727:0.140863:0.485691:0.140863:0.485691:0.125499:0.306727:0.125499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.284763:0.141649:0.297589:0.141649:0.297589:0.124513:0.284763:0.124513:0.000000
¿Dibuja dos rectas que :@0.093160:0.192000:0.247833:0.192000:0.247833:0.177101:0.093160:0.177101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sean paralelas y dos que :@0.082304:0.207088:0.247834:0.207088:0.247834:0.192189:0.082304:0.192189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sean perpendiculares :@0.101486:0.222175:0.247833:0.222175:0.247833:0.207276:0.101486:0.207276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.108521:0.163125:0.227756:0.163125:0.227756:0.146224:0.108521:0.146224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Pienso y progreso:@0.294883:0.332884:0.417347:0.332884:0.417347:0.317520:0.294883:0.317520:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Piensa en una actividad cotidiana en la que debas utilizar el concepto de pendiente.:@0.294883:0.351536:0.854135:0.351536:0.854135:0.336637:0.294883:0.336637:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las rectas  ::@0.287495:0.414951:0.382493:0.415323:0.382493:0.398934:0.287495:0.398562:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
LA xB yC:@0.365099:0.415323:0.472016:0.415323:0.472016:0.398962:0.365099:0.398962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
LA xB yC:@0.516925:0.415323:0.630439:0.415323:0.630439:0.398962:0.516925:0.398962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.371172:0.417327:0.376384:0.417327:0.376384:0.407829:0.371172:0.407829:0.000000
1:@0.394571:0.417327:0.399783:0.417327:0.399783:0.407829:0.394571:0.407829:0.000000
1:@0.432110:0.417327:0.437322:0.417327:0.437322:0.407829:0.432110:0.407829:0.000000
1:@0.471902:0.417327:0.477114:0.417327:0.477114:0.407829:0.471902:0.407829:0.000000
2:@0.523677:0.417327:0.528889:0.417327:0.528889:0.407829:0.523677:0.407829:0.000000
2:@0.549277:0.417327:0.554488:0.417327:0.554488:0.407829:0.549277:0.407829:0.000000
2:@0.589015:0.417327:0.594227:0.417327:0.594227:0.407829:0.589015:0.407829:0.000000
2:@0.630997:0.417327:0.636209:0.417327:0.636209:0.407829:0.630997:0.407829:0.000000
0;  :@0.493935:0.415323:0.516926:0.415323:0.516926:0.398934:0.493935:0.398934:0.000000:0.000000:0.000000:0.000000
0:@0.654550:0.415323:0.663543:0.415323:0.663543:0.398934:0.654550:0.398934:0.000000
::@0.533305:0.415323:0.536511:0.415323:0.536511:0.398934:0.533305:0.398934:0.000000
+:@0.411590:0.416001:0.421707:0.416001:0.421707:0.400428:0.411590:0.400428:0.000000
+:@0.449386:0.416001:0.459502:0.416001:0.459502:0.400428:0.449386:0.400428:0.000000
=:@0.480897:0.416001:0.491014:0.416001:0.491014:0.400428:0.480897:0.400428:0.000000
+:@0.567802:0.416001:0.577918:0.416001:0.577918:0.400428:0.567802:0.400428:0.000000
+:@0.607800:0.416001:0.617916:0.416001:0.617916:0.400428:0.607800:0.400428:0.000000
=:@0.641522:0.416001:0.651639:0.416001:0.651639:0.400428:0.641522:0.400428:0.000000
La posición relativa de dos rectas en el plano describe cómo están ubicadas una res-:@0.287495:0.431547:0.903681:0.431547:0.903681:0.415158:0.287495:0.415158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pecto de la otra. Pueden darse tres casos::@0.287495:0.448144:0.588599:0.448144:0.588599:0.431755:0.287495:0.431755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rectas coincidentes :@0.287495:0.477337:0.492030:0.477337:0.492030:0.455827:0.287495:0.455827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si todos los coeficientes de sus ecuaciones son proporcionales, es decir::@0.287495:0.500118:0.812068:0.500118:0.812068:0.483729:0.287495:0.483729:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.553163:0.520596:0.563059:0.520596:0.563059:0.504234:0.553163:0.504234:0.000000
A:@0.552064:0.540241:0.561960:0.540241:0.561960:0.523880:0.552064:0.523880:0.000000
B:@0.588395:0.520596:0.597241:0.520596:0.597241:0.504234:0.588395:0.504234:0.000000
B:@0.587296:0.540241:0.596142:0.540241:0.596142:0.523880:0.587296:0.523880:0.000000
C:@0.623366:0.520596:0.633280:0.520596:0.633280:0.504234:0.623366:0.504234:0.000000
C:@0.622267:0.540241:0.632181:0.540241:0.632181:0.523880:0.622267:0.523880:0.000000
1:@0.561225:0.522599:0.566436:0.522599:0.566436:0.513101:0.561225:0.513101:0.000000
2:@0.560808:0.542245:0.566020:0.542245:0.566020:0.532747:0.560808:0.532747:0.000000
1:@0.596200:0.522599:0.601412:0.522599:0.601412:0.513101:0.596200:0.513101:0.000000
2:@0.595784:0.542245:0.600996:0.542245:0.600996:0.532747:0.595784:0.532747:0.000000
1:@0.633163:0.522599:0.638374:0.522599:0.638374:0.513101:0.633163:0.513101:0.000000
2:@0.632746:0.542245:0.637958:0.542245:0.637958:0.532747:0.632746:0.532747:0.000000
=:@0.572795:0.530074:0.547937:0.530074:0.547937:0.514501:0.572795:0.514501:0.000000
=:@0.607771:0.530074:0.582912:0.530074:0.582912:0.514501:0.607771:0.514501:0.000000
En este caso   =  , :@0.287495:0.563595:0.437190:0.563595:0.437190:0.547206:0.287495:0.547206:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.383761:0.563595:0.391390:0.563595:0.391390:0.547234:0.383761:0.547234:0.000000
1:@0.391384:0.566759:0.396626:0.566759:0.396626:0.557204:0.391384:0.557204:0.000000
L m:@0.417080:0.563595:0.452522:0.563595:0.452522:0.547234:0.417080:0.547234:0.000000:0.000000:0.000000
2:@0.424706:0.566759:0.429949:0.566759:0.429949:0.557204:0.424706:0.557204:0.000000
1:@0.452520:0.566759:0.457763:0.566759:0.457763:0.557204:0.452520:0.557204:0.000000
 = :@0.457763:0.563595:0.477518:0.563595:0.477518:0.547206:0.457763:0.547206:0.000000:0.000000:0.000000
m:@0.478218:0.563595:0.492850:0.563595:0.492850:0.547234:0.478218:0.547234:0.000000
2:@0.492845:0.566759:0.498087:0.566759:0.498087:0.557204:0.492845:0.557204:0.000000
 y, para un sistema de ecuaciones, este tendría infinitas :@0.498088:0.563595:0.907698:0.563595:0.907698:0.547206:0.498088:0.547206:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
soluciones.:@0.287497:0.580192:0.368429:0.580192:0.368429:0.563803:0.287497:0.563803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rectas paralelas:@0.287495:0.609386:0.450212:0.609386:0.450212:0.587876:0.287495:0.587876:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las rectas son paralelas si los coeficientes de sus ecuaciones cumplen lo siguiente::@0.287495:0.632167:0.889281:0.632167:0.889281:0.615778:0.287495:0.615778:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.552326:0.651934:0.562221:0.651934:0.562221:0.635573:0.552326:0.635573:0.000000
A:@0.551227:0.671580:0.561122:0.671580:0.561122:0.655219:0.551227:0.655219:0.000000
B:@0.587558:0.651934:0.596403:0.651934:0.596403:0.635573:0.587558:0.635573:0.000000
B:@0.586459:0.671580:0.595304:0.671580:0.595304:0.655219:0.586459:0.655219:0.000000
C:@0.622843:0.651934:0.632757:0.651934:0.632757:0.635573:0.622843:0.635573:0.000000
C:@0.621743:0.671580:0.631657:0.671580:0.631657:0.655219:0.621743:0.655219:0.000000
1:@0.560387:0.653938:0.565599:0.653938:0.565599:0.644440:0.560387:0.644440:0.000000
2:@0.559970:0.673584:0.565182:0.673584:0.565182:0.664086:0.559970:0.664086:0.000000
1:@0.595363:0.653938:0.600574:0.653938:0.600574:0.644440:0.595363:0.644440:0.000000
2:@0.594946:0.673584:0.600158:0.673584:0.600158:0.664086:0.594946:0.664086:0.000000
1:@0.632635:0.653938:0.637847:0.653938:0.637847:0.644440:0.632635:0.644440:0.000000
2:@0.632218:0.673584:0.637430:0.673584:0.637430:0.664086:0.632218:0.664086:0.000000
=:@0.571958:0.661413:0.582075:0.661413:0.582075:0.645840:0.571958:0.645840:0.000000
≠:@0.606933:0.661413:0.617050:0.661413:0.617050:0.645840:0.606933:0.645840:0.000000
Bajo esta condición,   ||   y :@0.287495:0.694934:0.491350:0.694934:0.491350:0.678545:0.287495:0.678545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.435580:0.694934:0.443209:0.694934:0.443209:0.678573:0.435580:0.678573:0.000000
1:@0.443214:0.698098:0.448457:0.698098:0.448457:0.688543:0.443214:0.688543:0.000000
L:@0.462977:0.694934:0.470606:0.694934:0.470606:0.678573:0.462977:0.678573:0.000000
2:@0.470611:0.698098:0.475854:0.698098:0.475854:0.688543:0.470611:0.688543:0.000000
m:@0.490668:0.694934:0.505300:0.694934:0.505300:0.678573:0.490668:0.678573:0.000000
1:@0.505305:0.698098:0.510548:0.698098:0.510548:0.688543:0.505305:0.688543:0.000000
 = :@0.510549:0.694934:0.528921:0.694934:0.528921:0.678545:0.510549:0.678545:0.000000:0.000000:0.000000
m:@0.528239:0.694934:0.542871:0.694934:0.542871:0.678573:0.528239:0.678573:0.000000
2:@0.542874:0.698098:0.548117:0.698098:0.548117:0.688543:0.542874:0.688543:0.000000
 y, para un sistema de ecuaciones, este no tendría :@0.548117:0.694934:0.907655:0.694934:0.907655:0.678545:0.548117:0.678545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
solución.:@0.287495:0.711531:0.352821:0.711531:0.352821:0.695142:0.287495:0.695142:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rectas secantes:@0.287495:0.740725:0.446272:0.740725:0.446272:0.719215:0.287495:0.719215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dos rectas son secantes cuando se cortan en un solo punto y ocurre cuando,:@0.287495:0.763506:0.850858:0.763506:0.850858:0.747117:0.287495:0.747117:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.569152:0.783341:0.579047:0.783341:0.579047:0.767948:0.569152:0.767948:0.000000
A:@0.568046:0.802980:0.577942:0.802980:0.577942:0.787587:0.568046:0.787587:0.000000
B:@0.604422:0.783341:0.613268:0.783341:0.613268:0.767948:0.604422:0.767948:0.000000
B:@0.604422:0.802980:0.613268:0.802980:0.613268:0.787587:0.604422:0.787587:0.000000
1:@0.576952:0.785335:0.582163:0.785335:0.582163:0.776254:0.576952:0.776254:0.000000
2:@0.576535:0.804982:0.581746:0.804982:0.581746:0.795900:0.576535:0.795900:0.000000
1:@0.613572:0.785335:0.618784:0.785335:0.618784:0.776254:0.613572:0.776254:0.000000
2:@0.613080:0.804982:0.618292:0.804982:0.618292:0.795900:0.613080:0.795900:0.000000
≠:@0.588730:0.792820:0.598847:0.792820:0.598847:0.777247:0.588730:0.777247:0.000000
Estas rectas tienen sus pendientes distintas, es decir, :@0.287495:0.825035:0.672239:0.825035:0.672239:0.808646:0.287495:0.808646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.672239:0.825035:0.686870:0.825035:0.686870:0.808673:0.672239:0.808673:0.000000
1:@0.686869:0.828198:0.692112:0.828198:0.692112:0.818644:0.686869:0.818644:0.000000
 ≠ :@0.692111:0.825035:0.711165:0.825035:0.711165:0.808646:0.692111:0.808646:0.000000:0.000000:0.000000
m:@0.711165:0.825035:0.725797:0.825035:0.725797:0.808673:0.711165:0.808673:0.000000
2:@0.725797:0.828198:0.731039:0.828198:0.731039:0.818644:0.725797:0.818644:0.000000
.:@0.731039:0.825035:0.734245:0.825035:0.734245:0.808646:0.731039:0.808646:0.000000
Rectas perpendiculares:@0.287494:0.854229:0.523547:0.854229:0.523547:0.832719:0.287494:0.832719:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Son rectas secantes que cumplen con la siguiente condición::@0.287494:0.877010:0.734615:0.877010:0.734615:0.860621:0.287494:0.860621:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.501177:0.906037:0.515809:0.906037:0.515809:0.889676:0.501177:0.889676:0.000000
m:@0.550287:0.916880:0.564918:0.916880:0.564918:0.900519:0.550287:0.900519:0.000000
mm:@0.608500:0.906037:0.649944:0.906037:0.649944:0.889676:0.608500:0.889676:0.000000:0.000000
1:@0.514160:0.908041:0.519372:0.908041:0.519372:0.898543:0.514160:0.898543:0.000000
2:@0.563949:0.918886:0.569161:0.918886:0.569161:0.909388:0.563949:0.909388:0.000000
1:@0.621480:0.908041:0.626692:0.908041:0.626692:0.898543:0.621480:0.898543:0.000000
2:@0.648970:0.908041:0.654181:0.908041:0.654181:0.898543:0.648970:0.898543:0.000000
1:@0.557036:0.897275:0.566029:0.897275:0.566029:0.880886:0.557036:0.880886:0.000000
1:@0.683155:0.906044:0.692148:0.906044:0.692148:0.889655:0.683155:0.889655:0.000000
=−:@0.523165:0.906715:0.546900:0.906715:0.546900:0.891142:0.523165:0.891142:0.000000:0.000000
→:@0.582797:0.906715:0.600985:0.906715:0.600985:0.891142:0.582797:0.891142:0.000000
⋅:@0.628976:0.906715:0.633583:0.906715:0.633583:0.891142:0.628976:0.891142:0.000000
=−:@0.659492:0.906715:0.683227:0.906715:0.683227:0.891142:0.659492:0.891142:0.000000:0.000000
nidad de conocimientos:@0.306727:0.384510:0.480398:0.384510:0.480398:0.369146:0.306727:0.369146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.284892:0.385296:0.297460:0.385296:0.297460:0.368160:0.284892:0.368160:0.000000
En el desplazamiento de barcos o aviones, es crucial predecir la posición relativa en-:@0.287490:0.168340:0.903596:0.168340:0.903596:0.151951:0.287490:0.151951:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tre dos trayectorias para identificar si los móviles se cruzaran en algún punto, como :@0.287490:0.184936:0.907744:0.184936:0.907744:0.168547:0.287490:0.168547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
veremos en el siguiente ejemplo::@0.287490:0.201533:0.530087:0.201533:0.530087:0.185144:0.287490:0.185144:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dos barcos salen al mismo tiempo desde puntos diferentes y siguen trayectorias rec-:@0.287490:0.225252:0.903617:0.225252:0.903617:0.208863:0.287490:0.208863:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tilíneas: el barco A parte del punto (2, 3) km con una velocidad :@0.287490:0.244434:0.744859:0.244434:0.744859:0.228045:0.287490:0.228045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.746756:0.244373:0.754495:0.244373:0.754495:0.228012:0.746756:0.228012:0.000000
kmh:@0.830049:0.244373:0.872856:0.244373:0.872856:0.228012:0.830049:0.228012:0.000000:0.000000:0.000000
A:@0.755918:0.246377:0.761653:0.246377:0.761653:0.236894:0.755918:0.236894:0.000000
:@0.748170:0.233080:0.762746:0.233080:0.762746:0.217023:0.748170:0.217023:0.000000:0.000000
:@0.753034:0.233080:0.760590:0.233080:0.760590:0.217023:0.753034:0.217023:0.000000
=:@0.767068:0.245050:0.777185:0.245050:0.777185:0.229478:0.767068:0.229478:0.000000
−:@0.803186:0.245050:0.813303:0.245050:0.813303:0.229478:0.803186:0.229478:0.000000
(,:@0.779783:0.244373:0.793143:0.244373:0.793143:0.227984:0.779783:0.227984:0.000000:0.000000
) 1:@0.820833:0.244373:0.823436:0.244373:0.823436:0.227984:0.820833:0.227984:0.000000:0.000000:0.000000
/:@0.854187:0.244373:0.860655:0.244373:0.860655:0.227984:0.854187:0.227984:0.000000
1:@0.783872:0.244373:0.792865:0.244373:0.792865:0.227984:0.783872:0.227984:0.000000
 y el :@0.875225:0.244447:0.907676:0.244447:0.907676:0.228058:0.875225:0.228058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
barco B parte del punto (–1 , 6) km con una velocidad :@0.287494:0.263394:0.684806:0.263394:0.684806:0.247006:0.287494:0.247006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.687005:0.263558:0.694745:0.263558:0.694745:0.247197:0.687005:0.247197:0.000000
kmh:@0.772288:0.263558:0.815095:0.263558:0.815095:0.247197:0.772288:0.247197:0.000000:0.000000:0.000000
B:@0.695539:0.265562:0.700665:0.265562:0.700665:0.256080:0.695539:0.256080:0.000000
:@0.688419:0.252265:0.702203:0.252265:0.702203:0.236208:0.688419:0.236208:0.000000:0.000000
=−:@0.706533:0.264236:0.735188:0.264236:0.735188:0.248663:0.706533:0.248663:0.000000:0.000000
( 22  :@0.719248:0.263558:0.772285:0.263558:0.772285:0.247169:0.719248:0.247169:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, ):@0.743757:0.263558:0.767956:0.263558:0.767956:0.247169:0.743757:0.247169:0.000000:0.000000:0.000000
/:@0.796427:0.263558:0.802895:0.263558:0.802895:0.247169:0.796427:0.247169:0.000000
a):@0.287495:0.287117:0.302403:0.287117:0.302403:0.270217:0.287495:0.270217:0.000000:0.000000
  Halla la ecuación general de la trayectoria de ambos barcos.:@0.302403:0.287117:0.753344:0.287117:0.753344:0.270728:0.302403:0.270728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b):@0.287495:0.307282:0.303712:0.307282:0.303712:0.290381:0.287495:0.290381:0.000000:0.000000
  Determina si las trayectorias son paralelas, coincidentes o secantes.:@0.303712:0.307282:0.805563:0.307282:0.805563:0.290893:0.303712:0.290893:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Posiciones relativas de las rectas en :@0.286308:0.078354:0.814739:0.078354:0.814739:0.044801:0.286308:0.044801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.814739:0.079515:0.841348:0.079515:0.841348:0.044304:0.814739:0.044304:0.000000
2:@0.841338:0.066259:0.852038:0.066259:0.852038:0.046698:0.841338:0.046698:0.000000
5 :@0.094760:0.108603:0.183816:0.108603:0.183816:0.011514:0.094760:0.011514:0.000000:0.000000
©Shutterstock:@0.070380:0.316771:0.070380:0.273945:0.058469:0.273945:0.058469:0.316771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las matemáticas permiten :@0.072616:0.371902:0.234662:0.371902:0.234662:0.358493:0.072616:0.358493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a los navegantes orientarse, :@0.072616:0.384474:0.241477:0.384474:0.241477:0.371065:0.072616:0.371065:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
planificar rutas, corregir :@0.072616:0.397046:0.215847:0.397046:0.215847:0.383636:0.072616:0.383636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
desvíos y llegar con seguridad :@0.072616:0.409617:0.256629:0.409617:0.256629:0.396208:0.072616:0.396208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a su destino, tanto en el mar :@0.072616:0.422189:0.245323:0.422189:0.245323:0.408780:0.072616:0.408780:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como en el aire.:@0.072616:0.434761:0.167600:0.434761:0.167600:0.421352:0.072616:0.421352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rectas coincidentes:@0.072616:0.607503:0.191889:0.607503:0.191889:0.594094:0.072616:0.594094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.108631:0.575520:0.112765:0.575520:0.112765:0.568251:0.108631:0.568251:0.000000
x:@0.252319:0.574984:0.255428:0.574984:0.255428:0.569042:0.252319:0.569042:0.000000
y:@0.107249:0.486620:0.110358:0.486620:0.110358:0.480678:0.107249:0.480678:0.000000
Rectas paralelas:@0.072616:0.768819:0.167572:0.768819:0.167572:0.755410:0.072616:0.755410:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.108631:0.735055:0.112765:0.735055:0.112765:0.727786:0.108631:0.727786:0.000000
x:@0.252319:0.733908:0.255428:0.733908:0.255428:0.727966:0.252319:0.727966:0.000000
y:@0.107249:0.646153:0.110358:0.646153:0.110358:0.640211:0.107249:0.640211:0.000000
Rectas secantes:@0.072616:0.930509:0.167027:0.930509:0.167027:0.917100:0.072616:0.917100:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.108631:0.896373:0.112765:0.896373:0.112765:0.889104:0.108631:0.889104:0.000000
x:@0.252319:0.895838:0.255428:0.895838:0.255428:0.889896:0.252319:0.889896:0.000000
y:@0.109266:0.807475:0.112375:0.807475:0.112375:0.801533:0.109266:0.801533:0.000000
A:@0.085521:0.843736:0.089525:0.843736:0.089525:0.837794:0.085521:0.837794:0.000000
M.5.2.11. :@0.298180:0.946788:0.353423:0.946788:0.353423:0.934496:0.298180:0.934496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Determinar la posición relativa de dos rectas en R  (rectas paralelas, que se cortan, perpendiculares) en :@0.353785:0.946788:0.906587:0.946788:0.906587:0.934868:0.353785:0.934868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.619195:0.942389:0.623007:0.942389:0.623007:0.935441:0.619195:0.935441:0.000000
la resolución de problemas (por ejemplo: trayectoria de aviones o de barcos para determinar si se interceptan).:@0.298185:0.958103:0.886212:0.958103:0.886212:0.946184:0.298185:0.946184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000