ZXTape! 2p$CURSOS EDUCATIVOS. MATEMATICAS (4/4)MONSERGAME (EDUCATIONAL)+D.L. M-41231-1985. TZXed by johnny farragutMATEMATICA**x,&"":21,0;:"MODULO E"  @R    @! @`d&$ $$$   @! d&$ $$d$@   @!   @! d&$ $$d$@   @!    @ %# $$d$@   @!    @ %# ##   @!    @ ##%# ##   @! @`##$$$##   @! @`##$$$<<0 0<<0 0 0 00 ?00 ?0? 0 0 ?0 0 0 <0 ?0 30 ?30 00 0 0 00 0 0 0 0 BBB<<0 0<<0 0 0 00 ?00 ?0? 0 0 ?0 0 0 BBFB@DBBBB<<0 0<<0 0 0 00 ?00 ?0? 0 0 ?0 0 0 BB<<<<<0 0<<0 0 0 00 ?00 ?0? 0 0 ?0 0 0 <999999999999999999999999999999999::::::::::::::::::::::::::::::99:::::999999999999999999999::::99:::::999999999999999999999::::99::::::::::::::::::::::::::::::9999999999999999999999999999999999::::::::::::::::::::::::::::::99:::::<<<<<<<<<<<<<<<<<<<::::::99:::::<<<<<<<<<<<<<<<<<<<::::::99:::::<<<<<<<<<<<<<<<<<<<::::::99:::::<<<<<<<<<<<<<<<<<<<::::::99:::::::::::<<<<<<<::::::::::::99:::::::::::<<<<<<<::::::::::::99:::::::::::<<<<<<<::::::::::::99:::::::::::<<<<<<<::::::::::::99::::::::::::::::::::::::::::::99::::::::::::::::::::::::::::::99::::::::::::::::::::::::::::::99::::::::::::::::::::::::::::::99::::::::::::::::::::::::::::::99::::88888888888888888888::::::9999999999999999999999999999999998888888888888888888888888888888888888888888888888888888888888888MODULO E DԁF+"Programmed by Tony Topliss." 7:0::100d g1:1:64999:6,5;"MODULO E CASI LISTO":"mat code 5":1 Z123658j\,0::6;2,2;"MODULO APRENDIZAJE MATEMATICAS";3,13 ;"22-27";7;'"22. Probabilidad-Definicion"''"23. Probabilidad-Regla de suma"''"24. Probabilidad-Regla de Multi- plicacion"''"25. Trigonometria"''"26. Relacion"''"27. Trigonometria,3-Dimensiones": dq90Z:18,0;" Cuando vea el mensaje inferior,pulse @ para dejar el modulo. ":8990 # ab$=" ":4:d$(7,16):k$(8,16):qu=0:8 ٰ90Z:.1}L,35#:16,0;" ENTRA el numero del modulo con el que deseas trabajar:- (0 para finalizar) ":q$=" ":n=0 ""986 /0:i$=:=480q$=" "8999'# @i$480Ưi$579ůi$=12 ůi$=13 990 ;.1}L,-5:2:.4L,-20:984 i$=12 984 Si$=13 n=0.1}L,-5:2:.4L,-20:984 *i$=13 qu=q$-22:998 `n=n+1:q$=q$+i$:q$>27.1}L,-5:2:.4L,-20:984 P.1}L,35#:17,27;8;1;7;q$:986 Iq$<22.1}L,-5:2:.4L,-20:984 qu=qu+1 r=0::.1}L,35#:6;0,10 ;"MATEMATICAS";2;7;0,0;"Modulo ";qu+21:6000p+qu:a,qi1,qi2,qi3,qi4,qi5,qi6,qi7,qi8,qi9,qi10,qi11,qi12,qi13,qi14,qi15,qi16,qi17,qi18,qi19:20:.1}L,35#:17,0;3;7;1;" Desea repasar antes de respon- der las preguntas? Pulse S/N. ":6100+20*qu:20 E.1}L,35#:65001,11 :65000:65040 ^n=1a:n=qi1n=qi2n=qi3n=qi4n=qi5n=qi6n=qi7n=qi8n=qi96100+n+20*qu .1}L,35#:65001,12 :65000:65040:12 ,0;"PREGUNTAS";12 ,16;"AYUDAS" 7000X+30*qu+n:vval,g$,u$,x,y,nlsq:l=1nlsq:d$(l):12 +l,0;d$(l):l::l=1(g$+u$+*2):y,x+l-1;"*";:l:1100L an=qi10n=qi11n=qi12n=qi13n=qi14n=qi15n=qi16n=qi17n=qi18n=qi196500d+n+30*qu Jn:2000:8990#:65001,22:65000:984 L5ph=0:hh=0:bb=0:hint=0:i Q8hint120,0;"PRUEBA DE NUEVO " Sl0,4;"escribe tu respuesta: ";h$:v$="":u$""0,4;"escribe las unidades: ";v$ VCa$=h$+v$:a$>g$+u$Ʊa$>(16-x)a$=a$(116-x) X20,0;" ";y,x;5;b$(1̱g$+u$+1);1;7;y,x;a$:h$+v$=g$+u$1138r Zvval=01160 \4vct=0:vctt=0:h$=01180 ^1l=1̱h$:h$(l)=46.vct=vct+1 _$h$(l)=47/vctt=vctt+1 `-h$(l)<46.ůh$(l)>5791180 b-h$(l)>47/Ưh$(l)<58:1130j cl=h$1180 e#h$(l)=46.l=h$1180 f%h$(l+1)=47/1180 j)l:vct>1vctt>11180 k#h$(1)=47/1180 lh$=g$v$=u$1138r mh$ɰg$1180 n 1165 r20,1;2;6;1;1;"CORRECTO";:" ":l=14:.1}L,34":.1}L,30:l:20:8990#:1150~ t 1160 ~hh=0r=r+1  1195 h$g$1180 8v$u$20,1;0;7;1;"UNIDADES!":.1}L,-5:2:.4L,-20:hint=hint+1:8990#::l=1nlsq:5;0;12 +l,0;d$(l):l:l=1(g$+u$+(*2)):y,x+l-1;"*":l:hint=2hh=hh+1:1200  hint=1:hh8ph=0 il=120:.01z# =,35#:.01z# =,25:l:m=1j:k$(m):hh=im=jbb=1 &bb;12 +ph+m,16;k$(m):m  ph=ph+j *20,7;5;" ": 65001,22:65000:5,0;" En este modulo consiguio:- respuestas correctas sin ayuda. ";9 ,0;" Si necesita mas ayuda, trabaje con las siguientes secciones de AYUDA AL ESTUDIO MONSER. " "a=0r=1:a=12 ұ9 ;6,10 ;r;" sobre ";a:r/a.8L3,11 ;"MUY BIEN":j=15:.1}L,16:.1}L,24:.1}L,20:j 2000+10 *qu: 313 ,0;" Ejercicio 13a, pagina 108.": $13 ,0;" Pagina 109.": 313 ,0;" Ejercicio 13b, pagina 113.": H1,23;" ";13 ,0;" Capitulo 17 pagina 148.": )13 ,0;" Paginas 159-163.":  313 ,0;" Ejercicio 18c, pagina 169.": q10 ,6,.8L,.9ffff,.1}L,1.1 ,.2~L,.5,.5,.5,.1}L,.5,1.1 ,1.2,1.43333,1.9s333,2.4,2.5 ,.9ffff,.1}L r6,4,.8L,.9ffff,.1}L,1.1 ,.2~L,.5,.5,.5,.1}L,.5,1.1 ,1.2,1.43333,1.9s333,2.4,2.5 ,.9ffff,.1}L s19,10 ,.8L,.9ffff,.1}L,1.1 ,.2~L,.5,.5,.5,.1}L,.5,1.1 ,1.2,1.43333,1.9s333,2.4,2.5 ,.9ffff,.1}L t15,6,11 ,.9ffff,.1}L,1.1 ,.2~L,.5,.5,.5,.1}L,.5,1.1 ,1.2,1.43333,1.9s333,2.4,2.5 ,.9ffff,.1}L u4,3,.8L,.9ffff,.1}L,1.1 ,.2~L,.5,.5,.5,2,3,4,1.2,1.43333,1.9s333,2.4,2.5 ,.9ffff,.1}L v12 ,5,.8L,.9ffff,.1}L,1.1 ,.2~L,.5,.5,.5,.1}L,.5,1.1 ,1.2,1.43333,1.9s333,2.4,2.5 ,.9ffff,.1}L V1,4;6;"PROBABILIDAD-DEFINICION":.1}L,35#:8521I!: 65001,22:65000:1,35#:5,0;"2. Se elige un numero al azar de:-"'" 1, 1, 1, 2, 2, 3, 4, 5": \1,2;6;"PROBABILIDAD-REGLA DE LA SUMA":.1}L,35#:8541]!: 65001,15:65000:1,35#:8,0;"2. Se elige un numero al azar de:-"'"1, 2, 2, 3, 3, 3, 5, 5, 5, 7, 7": 65001,15:65000:1,35#:8,0;"2. Se elige un numero al azar de :-"'"1, 2, 2, 3, 3, 3, 5, 5, 5, 7, 7": _1,0;6;"PROBABI.-REGLA DE MULTIPLICACION":.1}L,35#:8561q!:  65001,15:65000:1,35#:7,0;"2. Se eligen unos libros, sin reemplazarlos, de una estante- ria que contiene: 7 libros en frances, 8 en aleman y 5 en ita-liano"'" (ENTRA fracciones; ej. 6/18).": %L1,9 ;6;"TRIGONOMETRIA":.1}L,35#:8581!: *065001,22:65000:8700! +1;11 ,21;"10cm";5,15;"7.5cm";9 ,14;"51.2":1,23;"B":1,35#:2,0;"2."'" En el triangulo"'"ABC,BX es"'"perpendicular"'"a AC,AB=7.5cm,"'"AC=10cm y"'"5)= /10",1,3,"Hay 4","numeros mayores","que 5 en el grupo E."," Pr(>5)=4/10" {0,"7","",10 ,14,2,"e."," Pr(>2)= /10",1,3,"Hay 7","numeros mayores","que 2 en el grupo E."," Pr(>2)=7/10" ||0,"2","",10 ,14,2,"a."," Pr(2)= /8",1,3,"Hay 2 2","en el grupo E."," Pr(2)=2/8" }|0,"1","",10 ,14,2,"b."," Pr(5)= /8",1,3,"Hay 1 5","en el grupo E."," Pr(5)=1/8" ~0,"3","",10 ,14,2,"c.","Pr(dif.)= /8",1,3,"Hay 3 numeros","diferentes en el grupo E."," Pr(dif.)=3/8" 0,"0","",10 ,14,2,"d."," Pr(>5)= /8",1,3,"No hay numeros","mayores que 5 en","el grupo E."," Pr(>5)=0/8" 0,"3","",10 ,14,2,"e."," Pr(>2)= /8",1,3,"Hay 3 numeros","mayores que 2 en","el grupo E."," Pr(>2)=3/8" 1,"3/7","",11 ,14,5,"a.","Pr(3 o 5)=","","ENTRA fraccion;","Ej. 5/9 .",2,2," Pr(3 o 5)","=Pr(3)+Pr(5)",2,"=1/7 + 2/7","=3/7" 1,"2/7","",11 ,14,5,"b.","Pr(2 o 3)=","","ENTRA fraccion;","Ej. 5/9 .",2,2," Pr(2 o 3)","=Pr(2)+Pr(3)",2,"=1/7 + 1/7","=2/7" 1,"3/7","",11 ,14,5,"c.","Pr(5 o 7)=","","ENTRA fraccion;","Ej. 5/9 .",2,2," Pr(5 o 7)","=Pr(5)+Pr(7)",2,"=2/7 + 1/7","=3/7" 1,"6/11","",11 ,14,5,"a.","Pr(3 o 5)=","","ENTRA fraccion;","Ej. 5/9 .",2,2," Pr(3 o 5)","=Pr(3)+Pr(5)",2,"=3/11 + 3/11","=6/11" 1,"5/11","",11 ,14,5,"b.","Pr(2 o 3)=","","ENTRA fraccion;","Ej. 5/9 .",2,2," Pr(2 o 3)","=Pr(2)+Pr(3)",2,"=2/11 + 3/11","=5/11" 1,"5/11","",11 ,14,5,"c.","Pr(5 o 7)=","","ENTRA fraccion;","Ej. 5/9 .",2,2," Pr(5 o 7)","=Pr(5)+Pr(7)",2,"=3/11 + 2/11","=5/11" u1,"5/12","",1,15,3,"a.","Pr(1ro un toffe)","=",1,2,"Pr(1ro un toffe)"," =5/12" 1,"5/12","",1,16,4,"b.","Pr(1ro un toffe","y 2do de menta)","= X .",1,2,"Pr(1ro de fresa)"," =5/12" 1,"3/11","",6,16,4,"b.","Pr(1ro un toffe","y 2do de menta)","=5/12X",1,3,"[Solo quedan 11]","Pr(2do de menta)"," =3/11" 1,"5/12","",1,16,4,"c.","Pr(1ro un toffe","y 2do un toffe)","= X .",1,2,"Pr(1ro un toffe)"," =5/12" 1,"4/11","",6,16,4,"c.","Pr(1ro un toffe","y 2do un toffe)","=5/12X",1,5,"[Solo quedan 11 de los","que 4 son","toffes]","Pr(2do un toffe)"," =4/11" 1,"3/12","",1,16,4,"d.","Pr(1ro de menta","y 2do de menta)","= X .",1,2,"Pr(1ro de menta)"," =3/12" 1,"2/11","",6,16,4,"d.","Pr(1ro de menta","y 2do de menta)","=3/12X",1,5,"[Solo quedan 11 de los","que 2 son","de menta]","Pr(2do de menta)"," =2/11" 1,"3/12","",1,16,4,"e.","Pr(1ro de menta","y 2do un toffe)","= X .",1,2,"Pr(1ro de menta)"," =3/12" 1,"5/11","",6,16,4,"e.","Pr(1ro de menta","y 2do un toffe)","=3/12X",1,5,"[Solo quedan 11 de los","que 5 son","toffes]","Pr(2do un toffe)"," =5/11" 1,"7/20","",1,16,4,"a.","Pr(1ro frances","y 2do frances)","= X .",1,2,"Pr(1ro frances)"," =7/20" 1,"6/19","",6,16,4,"a.","Pr(1ro frances","y 2do frances)","=7/20X",1,2,"Pr(2do frances)"," =6/19" 1,"7/20","",1,16,4,"b.","Pr(1ro frances","y 2do italiano)","= X .",1,2,"Pr(1ro frances)"," =7/20" 1,"5/19","",6,16,4,"b.","Pr(1ro frances","y 2do italiano)","=7/20X",1,2,"Pr(2do italiano)"," =5/19" 1,"7/20","",1,16,4,"c.","Pr(1ro frances","y 2do aleman)","= X .",1,2,"Pr(1ro frances)"," =7/20" 1,"8/19","",6,16,4,"c.","Pr(1ro frances","y 2do aleman)","=7/20X",1,2,"Pr(2do aleman)"," =8/19" Œ1,"8/20","",1,16,4,"d.","Pr(1ro aleman","y 2do frances)","= X .",1,2,"Pr(1ro aleman)"," =8/20" Ç1,"7/19","",6,16,4,"d.","Pr(1ro aleman","y 2do frances)","=8/20X",1,2,"Pr(2do frances)"," =7/19" č1,"8/20","",1,16,4,"e.","Pr(1ro aleman","y 2do italiano)","= X .",1,2,"Pr(1ro aleman)"," =8/20" ʼn1,"5/19","",6,16,4,"e.","Pr(1ro aleman","y 2do italiano)","=8/20X",1,2,"Pr(2do italiano)"," =5/19" ќ0,"2.57","cm",6,14,2,"a."," BX=",3,1,"40=BX/AB",1,"BX=ABx40",3," =4x0.6428"," =2.5712"," =2.57" ҄0,"3.06","cm",6,14,2,"b."," AX=",2,1,"AX=AB40",3,"AX=4x0.7660"," =3.064"," =3.06" ӄ0,"2.94","cm",6,14,2,"c."," XC=",2,1," XC=AC-AX",3," =6-3.064"," =2.936"," =2.94" Ԯ0,"41.2","",6,15,3,"d."," Angulo BCX,"," 5)=_  12":8990# !Q 9120# !R""8530R! !S+5:0:="S"Ŧ="s"8524L! !T"N"Ʀ"n"8530R! !W65001,22:65000:1,35#:5,0;"1. Se elige un numero al azar entre:-"''" 1, 2, 2, 3, 4, 5, 7, 8, 8, 10": !]""8541]! !^+5:0:="N"Ŧ="n"8551g! !_"S"Ʀ"s"8541]! !`7.1}L,35#:65001,22:65000 !a3,0;" Se elige un numero al azar:"'" 1, 2, 2, 2, 3, 3, 4, 4, 4, 4":8990#:7,0;"Pr(2)=_, ya que hay 3 2 entre  10 10 numeros.";5,5;"2, 2, 2":8990#:5,5;"2, 2, 2, 3, 3";10 ,0;"Pr(3)=_, ya que hay 2 3 entre  10 10 numeros.":8990# !bN5,5;"2, 2, 2";13 ,0;"Pr(2 o 3)=_, ya que hay 5 2  o  10 3 pero ningun numero es a la vez2 y 3.":8990#:5,2;"1, 2, 2, 2,";17,0;"Igualmente;"'"Pr(1 o 3)=_.  10":8990# !c65001,22:65000:3,0;" Donde dos sucesos,A y B,son mu-tuamente exclusivos e indepen- dientes,"'" Pr(A o B)=Pr(A)+Pr(B)":8990#:6,19;"+":9120# !d""8548d! !e+5:0:="S"Ŧ="s"8544`! !f"N"Ʀ"n"8548d! !g65001,15:65000:1,35#:8,0;"1. Se elige un numero al azar entre:-"'" 1, 2, 3, 5, 5, 7, 9": !q""8561q! !r+5:0:="N"Ŧ="n"8576! !s"S"Ʀ"s"8561q! !t7.1}L,35#:65001,22:65000 !u83,0;" Cuales son los resultados posibles cuando arrojamos a la vez undado y una moneda?":8990#:i=0112p112p:i+32 ,119w:6;23,0:6;0,-23:6;-23,0:6;0,23:i+99c,108l,12 :i !v8,5;"1";8,12 ;"C";8,15;"o";8,19;"1";8,26;"+":8990# !wt8,5;"2";8,12 ;"C";8,19;"2";8,26;"+":8990# !x8,5;"3";8,12 ;"C";8,19;"3";8,26;"+"'''"etc."''"La serie completa de posibilidades se escribe:"'"(1,C),(2,C),(3,C),(4,C),(5,C), (6,C),(1,+),(2,+),(3,+),(4,+), (5,+),(6,+)":8990# !y/65001,18:65000:6,0;" La serie completa de posibilidades se escribe;"'"(1,C),(2,C),(3,C),(4,C),(5,C), (6,C),(1,+),(2,+),(3,+),(4,+), (5,+),(6,+)"''" De estos 12 resultados,en 1/6 de ellos el dado saco 1, en 1/2 de ellos la moneda saco C.":8990# !z16,0;"Pr(1 y H)=X=_, solo uno de  6 2 12 los 12 resultados reunen ambos requisitos.":8990# !{L11 ,0;" Pr(2 y C)=X=_,(solo 1 de 6 2 12 los 12).Pr(6 y +)=X=_,(solo 1 6 2 12 de los 12).Pr(par y C)=X=_,(3 6 2 12 de los 12).Pr(>4 y C)=X=_,(2 6 2 12 de los 12)":8990# !|65001,22:65000:3,0;" La Regla de Multiplicacion es que si A y B son sucesos independientes,"'" Pr(A y B)=Pr(A).Pr(B)":9120# !}""8573}! !~+5:0:="S"Ŧ="s"8564t! !"N"Ʀ"n"8573}! !65001,15:65000:1,35#:7,0;"1. Se eligen caramelos entre 5 toffes,4 de chocolate y 3 de menta sin reponerlos."'" (ENTRA fracciones; ej. 6/18).": !""8581! !+5:0:="N"Ŧ="n"8586! !"S"Ʀ"s"8581! !.1}L,35#:65001,22:65000:5,0;" Si tenemos un triangulo que tiene un angulo recto,solo necesitamos usar la definicion de seno, coseno y tangente para hallar los lados y angulos pedidos.":8990#:65000 !7;17,0;" ":8700!:1;11 ,21;"6cm";5,15;"4cm";9 ,14;"40":1,35#:2,0;"1."'" En el triangulo"'"ABC,BX es"'"perpendicular"'"a AC,AB=4cm,"'"AC=6cm y"'"pPp8A8y9BBB9PLB q #$RR| P pd<*]\"_\C*]\~}t[3*a\Þ*x\#"xMODULO F 2Ž#47:0::100d g1:1:64999:6,5;"MODULO F CASI LISTO":"mat code 6":1 Z:6;2,0;" MODULOS APRENDIZAJE MATEMATICAS";3,13 ;"28-30";7;'''"28. Determinante e inversa de matrices 2 x 2"''"29. Transformacion de matrices"''"30. Hallar la matriz para descri bir una transformacion": dq90Z:18,0;" Cuando vea el mensaje inferior,pulse @ para dejar el modulo. ":8990 # rattmpts=2:b$=" ":4:d$(7,16):k$(7,16):qu=0:8 ٲ90Z:.1}L,35#:16,0;" ENTRA el numero del modulo con el que deseas trabajar:- (0 para finalizar) ":q$=" ":n=0 ""986 /0:i$=:=480q$=" "8999'# @i$480Ưi$579ůi$=12 ůi$=13 990 ;.1}L,-5:2:.4L,-20:984 i$=12 984 Si$=13 n=0.1}L,-5:2:.4L,-20:984 *i$=13 qu=q$-28:998 `n=n+1:q$=q$+i$:q$>30.1}L,-5:2:.4L,-20:984 P.1}L,35#:17,27;8;1;7;q$:986 Iq$<28.1}L,-5:2:.4L,-20:984 qu=qu+1 r=0::.1}L,35#:6;0,10 ;"MATEMATICAS";2;7;0,0;"Modulo ";qu+27:6000p+qu:a,qi1,qi2,qi3,qi4,qi5,qi6,qi7,qi8,qi9,qi10,qi11,qi12,qi13,qi14,qi15,qi16,qi17,qi18,qi19:20:.1}L,35#:17,0;3;7;1;" Deseas repasar antes de respon-der las preguntas? Pulsa S/N. ":6100+20*qu:20 E.1}L,35#:65001,11 :65000:65040 ^n=1a:n=qi1n=qi2n=qi3n=qi4n=qi5n=qi6n=qi7n=qi8n=qi96100+n+20*qu .1}L,35#:65001,12 :65000:65040:12 ,0;"PREGUNTAS";12 ,16;"AYUDAS" 7000X+30*qu+n:attmpts,vval,g$,u$,x,y,nlsq:l=1nlsq:d$(l):12 +l,0;d$(l):l::l=1(g$+u$):y,x+l-1;"*";:l:1100L an=qi10n=qi11n=qi12n=qi13n=qi14n=qi15n=qi16n=qi17n=qi18n=qi196500d+n+30*qu Jn:2000:8990#:65001,22:65000:984 L5ph=0:hh=0:bb=0:hint=0:i Q:hint120,0;"PRUEBA DE NUEVO " Sl0,5;"escribe la respuesta: ";h$:v$="":u$""1,3;"escribe las unidades: ";v$ V<a$=h$:h$>g$Ʊh$>(16-x)a$=h$(116-x) X20,0;" ";y,x;5;b$(1̱g$+u$);1;7;y,x;a$;v$:h$+v$=g$+u$1138r Zvval=01160 \4vct=0:vctt=0:h$=01180 ^1l=1̱h$:h$(l)=46.vct=vct+1 _$h$(l)=45-vctt=vctt+1 `Mh$(l)<480Ưh$(l)46.Ưh$(l)45-ůh$(l)>5791180 b#h$(l)=45-l=h$1180 d#h$(l)=46.l=h$1180 j)l:vct>1vctt>11180 kh$=g$v$=u$1138r lh$ɰg$1180 m 1165 r20,1;2;6;1;1;"CORRECTO";:" ":l=14:.1}L,34":.1}L,30:l:20:8990#:1150~ t 1160 ~hh=0r=r+1  1195 h$g$1180 +v$u$20,1;0;7;1;"UNIDADES!":.1}L,-5:2:.4L,-20:hint=hint+1:8990#::l=1nlsq:5;0;12 +l,0;d$(l):l:l=1(g$+u$):y,x+l-1;"*":l:hint=attmptshh=hh+1:1200 (hint=attmpts-1:hh8ph=0 il=120:.01z# =,35#:.01z# =,25:l:m=1j:k$(m):hh=im=jbb=1 &bb;12 +ph+m,16;k$(m):m  ph=ph+j *20,7;5;" ": 65001,22:65000:5,0;" En este modulo consiguio:- respuestas correctas sin ayuda. ";9 ,0;" Si necesitas mas ayuda, trabajacon las siguientes secciones deAYUDA AL ESTUDIO MONSER. " "a=0r=1:a=12 ұ9 ;6,10 ;r;" sobre ";a:r/a.8L3,11 ;"MUY BIEN":j=15:.1}L,16:.1}L,24:.1}L,20:j 2000+10 *qu: ,13 ,0;" Cap. 20 pagina 179.": 213 ,0;" Ejercicio 21, pagina 187.": ,13 ,0;" Cap. 21 pagina 182.": q24,5,.8L,.9ffff,.1}L,1.1 ,.2~L,.5,.5,.5,.1}L,.5,1.1 ,1.2,1.43333,1.9s333,2.4,2.5 ,.9ffff,.1}L r10 ,3,5,6,8,10 ,.2~L,.5,.5,.5,5,10 ,1.1 ,1.2,1.43333,1.9s333,2.4,2.5 ,.9ffff,.1}L s12 ,7,.8L,.9ffff,.1}L,1.1 ,.2~L,.5,.5,.5,.1}L,6,12 ,1.2,1.43333,1.9s333,2.4,2.5 ,.9ffff,.1}L 1,0;6;" DETERMINANTE E INVERSA DE ";2,8;"MATRICES 2 X 2":.1}L,35#:8521I!: 65001,21:65000:1,35#:3,0;"2. Calcula las inversas de las siguientes matrices:-";5,7;"1 2";5,23;"1 -2";6,2;" =";6,18;" =";7,7;"3 8";7,23;"3 4":557,135:0,-23,/3:88X,135:0,-23,-/3:183,135:0,-23,/3:216,135:0,-23,-/3 _9 ,8;"2 3";9 ,23;"1 -3";10 ,2;" =";10 ,18;" =";11 ,7;"-2 1";11 ,23;"2 -4":557,103g:0,-23,/3:88X,103g:0,-23,-/3:183,103g:0,-23,/3:216,103g:0,-23,-/3: &1,4;6;"TRANSFORMACION DE MATRICES":.1}L,35#:8541]!:4,4;"Cual es 5";'" la imagen bajo";6,6;"de 0";5,30;"?":102f,143:0,-23,/3:112p,143:0,-23,-/3: .1}L,35#:8,6;"5 4";10 ,6;"0 3":45-,111o:0,-23,/4:58:,111o:0,-23,-/4:93],111o:0,-23,/4:106j,111o:0,-23,-/4:68D,100d:16,0:-4,4:4,-4:-4,-4:10 :4,13 ;"0";6,13 ;"5": y.1}L,35#:8,19;"0 -3";10 ,19;"5 4":149,111o:0,-23,/4:162,111o:0,-23,-/4:197,111o:0,-23,/4:220,111o:0,-23,-/4:172,100d:16,0:-4,4:4,-4:-4,-4: 65001,22:65000:1,35#:4,0;"2.";4,5;"Cual es 5 0.8 0.6";5,3;"la imagen bajo";5,30;"?";6,7;"de 0 0.6 -0.8":167,144:0,-23,/3:232,144:0,-23,-/3:103g,144:0,-23,/3:112p,144:0,-23,-/3: .1}L,35#:8,6;"5 4";10 ,6;"0 3":45-,111o:0,-23,/4:58:,111o:0,-23,-/4:93],111o:0,-23,/4:106j,111o:0,-23,-/4:68D,100d:16,0:-4,4:4,-4:-4,-4:10 :4,13 ;"0";6,13 ;"5": y.1}L,35#:8,19;"0 3";10 ,19;"5 -4":149,111o:0,-23,/4:162,111o:0,-23,-/4:197,111o:0,-23,/4:220,111o:0,-23,-/4:172,100d:16,0:-4,4:4,-4:-4,-4: 1,7;6;"HALLAR LA MATRIZ PARA";2,2;"DESCRIBIR UNA TRANSFORMACION":.1}L,35#:8561q!: 65001,21:65000:1,35#:4,0;"2."'" Halla la matriz que convierte"''" 1 0 0 -1"'" en y en"'" 0 1 1 0":15,119w:8750.":24,119w:8751/":71G,119w:8750.":80P,119w:8751/":159,119w:8750.":168,119w:8751/":215,119w:8750.":232,119w:8751/": .1}L,35#:65001,22:65000:8730":80P:1,35#:12 ,31;"X":80P:1,35#:6,29;"X":502:.1}L,35#:173,77M:64@,480:208,76L:-10 ,19,/4:209,76L:-10 ,19,/4:5,27;"(4,3)" 100d:1,35#:2,21;"X":80P:1,35#:4,15;"X":502:.1}L,35#:172,77M:-480,64@:172,112p:-19,-10 ,/4:172,113q:-19,-10 ,/4:4,0;"La "'"transformacion"'"es una ROTACION "'"de angulo"'"el senalado. ";3,12 ;"(-3,4)":8990#: 3.1}L,35#:65001,22:65000:8730":80P:1,35#:12 ,31;"X":80P:1,35#:6,29;"X":502:.1}L,35#:173,77M:81Q,27:-162,-546:5,27;"(4,3)" 7100d:1,35#:2,21;"X":80P:1,35#:20,27;"X":502:.1}L,35#:4,0;"la "'"transformacion "'"es una REFLEXION"'"en la linea "'"senalada. ";19,25;"(3,-4)":8990#: :65001,21:65000:8740$":8990#:8,30;"X":1,35#:164,148:80P,-80P:13 ,25;"X":100d:.1}L,35#:3,25;"X":1,35#:8,20;"X":8990#: 465001,21:65000:8740$":8990#:8,30;"X":1,35#:243,108l:-39',39',/2:3,25;"X":100d:1,35#:-39',-40(,/2:8,20;"X":8990#: wa2,0,"-2","",6,14,2,"a."," ||=",1,2,"3x6-4x5"," =-2" xd2,0,"38","",6,14,2,"b."," ||=",1,2,"3x6-(-4)x5"," =38" yg2,0,"-2","",6,14,2,"c."," ||=",1,2,"3x6-(-4)x(-5)"," =-2" ze2,0,"2","",6,14,2,"d."," ||=",1,2,"3x(-6)-(-4)x5"," =2" {2,0,"2","",6,16,4,"a."," ( )"," =_( )"," ( )",1,2,"1x8-2x3"," =2" |2,0,"8","",8,14,4,"a."," ( )"," =_( )"," 2( )",2,1," Cambia 1 y 8.",1," 8" }|2,0,"1","",11 ,16,4,"a."," (8 )"," =_( )"," 2( )",1,1," 1" ~2,0,"-2","",10 ,14,4,"a."," (8 )"," =_( )"," 2( 1)",2,1," Cambia signos.",1," -2" }2,0,"-3","",8,16,4,"a."," (8 -2)"," =_( )"," 2( 1)",1,1," -3" 2,0,"10","",5,16,4,"b."," ( )"," =_( )"," ( )",1,2,"1x4-(-2)x3"," =10" 2,0,"4","",8,14,4,"b."," ( )"," =_( )"," 10( )",2,1," Cambia 1 y 4.",1," 4" |2,0,"1","",11 ,16,4,"b."," (4 )"," =_( )"," 10( )",1,1," 1" 2,0,"2","",11 ,14,4,"b."," (4 )"," =_( )"," 10( 1)",2,1," Cambia signos.",1," 2" }2,0,"-3","",8,16,4,"b."," (4 2)"," =_( )"," 10( 1)",1,1," -3" 2,0,"8","",6,16,4,"c."," ( )"," =_( )"," ( )",1,2,"2x1-3x(-2)"," =8" 2,0,"1","",8,14,4,"c."," ( )"," =_( )"," 8( )",2,1," Cambia 2 y 1.",1," 1" |2,0,"2","",11 ,16,4,"c."," (1 )"," =_( )"," 8( )",1,1," 2" 2,0,"-3","",10 ,14,4,"c."," (1 )"," =_( )"," 8( 2)",2,1," Cambia signos.",1," -3" {2,0,"2","",8,16,4,"c."," (1 -3)"," =_( )"," 8( 2)",1,1," 2" 2,0,"2","",6,16,4,"d."," ( )"," =_( )"," ( )",1,2,"1x(-4)-(-3)x2"," =2" 2,0,"-4","",8,14,4,"d."," ( )"," =_( )"," 2( )",2,1," Cambia 1 y -4.",1," -4" |2,0,"1","",11 ,16,4,"d."," (-4 )"," =_( )"," 2( )",1,1," 1" 2,0,"3","",11 ,14,4,"d."," (-4 )"," =_( )"," 2( 1)",2,1,"Cambia signos.",1," 3" }2,0,"-2","",8,16,4,"d."," (-4 3)"," =_( )"," 2( 1)",1,1," -2" 2,1,"4","",9 ,14,4,"a. La imagen de"," (5) ( )"," ( )=( )"," (0) ( )",1,2,"0.8x5+(-0.6)x0"," =4" 2,1,"3","",9 ,16,4,"b. La imagen de"," (5) ( 4)"," ( )=( )"," (0) ( )",1,2,"0.6x5+0.8x0"," =3" 2,1,"-3","",8,14,4,"c. La imagen de"," (0) ( )"," ( )=( )"," (5) ( )",1,2,"0.8x0+(-0.6)x5"," =-3" 2,1,"4","",9 ,16,4,"d. la imagen de"," (0) (-3)"," ( )=( )"," (5) ( )",1,2,"0.6x0+0.8x5"," =4" 1,0,"1","",0,18,6,"e. Es la trans-","formacion una","ROTACION"," (pulse 1)","o una REFLEXION?"," (pulse 2)",1,1," Rotacion." 2,1,"4","",8,14,4,"a. La imagen de"," (5) ( )"," ( )=( )"," (0) ( )",1,2,"0.8x5+0.6x0"," =4" 2,1,"3","",9 ,16,4,"b. La imagen de"," (5) ( 4)"," ( )=( )"," (0) ( )",1,2,"0.6x5+(-0.8)x0"," =3" 2,1,"3","",9 ,14,4,"c. La imagen de"," (0) ( )"," ( )=( )"," (5) ( )",1,2,"0.8x0+0.6x5"," =3" 2,1,"-4","",8,16,4,"d. La imagen de"," (0) ( 3)"," ( )=( )"," (5) ( )",1,2,"0.6x0+(-0.8)x5"," =-4" 1,0,"2","",0,18,6,"e. Es la trans-","formacion una","ROTACION"," (pulse 1)","o una REFLEXION?"," (pulse 2)",1,1," Reflexion." s2,1,"0","",5,14,4,"a."," ( )"," ( )"," ( )",1,1," 0" t2,1,"-1","",7,14,4,"b."," ( 0 )"," ( )"," ( )",1,1," -1" t2,1,"-1","",4,16,4,"c."," ( 0 -1)"," ( )"," ( )",1,1," -1" r2,1,"0","",8,16,4,"d."," ( 0 -1)"," ( )"," (-1 )",1,1," 0" 1,0,"2","",0,18,6,"e. Es la trans-","formacion una","ROTACION"," (pulse 1)","o una REFLEXION?"," (pulse 2)",1,1," Reflexion." 2,0,"4","",1,19,6,"f. Esto se refle","ja en,","eje-x (pulse 1)","eje-y (pulse 2)","y-x=0 (pulse 3)","y+x=0 (pulse 4)",1,3,"Reflexion en","la linea;"," y+x=0" s2,1,"0","",5,14,4,"a."," ( )"," ( )"," ( )",1,1," 0" t2,1,"-1","",7,14,4,"b."," ( 0 )"," ( )"," ( )",1,1," -1" r2,1,"1","",5,16,4,"c."," ( 0 -1)"," ( )"," ( )",1,1," 1" r2,1,"0","",8,16,4,"d."," ( 0 -1)"," ( )"," ( 1 )",1,1," 0" 1,0,"1","",0,18,6,"e. Es la trans-","formacion una","ROTACION"," (pulse 1)","o una REFLEXION?"," (pulse 2)",1,1," Rotacion." 2,1,"90","",1,15,4,"f. Esto gira","hasta,"," grados"," a la izquierda.",1,3,"Rotacion a la","izquierda de"," 90 grados." !I""8521I! !J+5:0:="N"Ŧ="n"8539[! !K"S"Ʀ"s"8521I! !L7.1}L,35#:65001,21:65000 !MT3,0;" Dada una matriz (2 x 2)";5,15;"a b";7,15;"c d";6,10 ;" =":119w,135:0,-23,/3:153,135:0,-23,-/3:9 ,0;"llamamos a la expresion ad-bc determinante de , escrito det  o||.":8990# !N'12 ,15;"2 3";14,15;"4 5";13 ,7;"Si =":119w,79O:0,-23,/3:153,79O:0,-23,-/3:16,0;"||=2x5-3x4=":8990#:16,4;"2x5";12 ,15;"2";14,18;"5":8990#:16,4;"2x5-3x4";12 ,15;"2 3";14,15;"4 5":8990#:16,4;"2x5-3x4";12 ,15;"2 3";14,15;"4";16,12 ;"-2":8990# !O`65001,8:65000:12 ,15;"2 -3";14,15;"4 5";13 ,7;"Si =":119w,79O:0,-23,/3:153,79O:0,-23,-/3:16,0;"||=2x5-(-3)x4=":8990#:16,4;"2x5";12 ,15;"2";14,18;"5":8990#:16,4;"2x5-(-3)x4";12 ,15;"2 -3";14,15;"4 5":8990#:16,4;"2x5-(-3)x4=22 (ten cuidado con el signo -)";12 ,15;"2 3";14,15;"4":8990# !P65001,8:65000:12 ,15;"2 3";14,15;"4 6";13 ,7;"Si =":119w,79O:0,-23,/3:153,79O:0,-23,-/3:16,0;"||=2x6-3x4=0":8990#:17,0;" Todas las matrices cuyos deter-minantes son cero se llaman ma- trices singulares.":8990# !Qt65001,21:65000:3,0;" Para encontrar la inversa, deuna matriz 2 x 2, " !R5,15;"a b";7,15;"c d";6,8;" =":119w,135:0,-23,/3:153,135:0,-23,-/3:8990#:9 ,0;" Primero intercambia a y d.";5,15;"d";7,15;"c a":8990#:10 ,0;" Luego cambia los signos de b y c";5,15;" d-b";7,15;"-c a":8990# !S11 ,0;" Finalmente divide por ||.";6,8;"=__";5,16;"d-b";7,15;"-c a";7,11 ;"||":8990# !Ta65001,21:65000:3,0;" Para hallar el inverso, de ." !U5,16;"2 3";7,15;"-4-5";6,8;" =":119w,135:0,-23,/3:153,135:0,-23,-/3:8990#:9 ,0;" Primero intercambia 2 y -5.";5,15;"-5";7,15;"-4 2":8990#:10 ,0;" Luego cambia los signos de 3 y -4";5,15;"-5-3";7,15;" 4 2":8990# !V12 ,0;" Finalmente divide por ||.";6,8;"=__";5,15;"-5-3";7,15;" 4 2";7,11 ;" 2":8990#:13 ,0;" Si ||=0, no hay inversa, por tanto esas matrices no tienen inversa.":8990# !W65001,21:65000:3,0;" Comprueba siempre que,";5,15;"1 0";7,15;"0 1";6,7;". =":119w,135:0,-23,/3:153,135:0,-23,-/3:80P:.1}L,35#:12 ,9 ;"-5 -3 2 3 1 0"'" Aqui, ";14,7;"2 4 2 -4 -5 0 1";13 ,22;"=":71G,79O:0,-23,/3:112p,79O:0,-23,-/3:127,79O:0,-23,/3:168,79O:0,-23,-/3:191,79O:0,-23,/3:224,79O:0,-23,-/3:8990#:8995## !X""8536X! !Y+5:0:="S"Ŧ="s"8524L! !Z"N"Ʀ"n"8536X! ![1,35#:65001,21:65000:3,0;"1. Halla el determinante de lassiguientes matrices:-";5,7;"3 4";5,23;"3 -4";6,2;" =";6,18;" =";7,7;"5 6";7,23;"5 6":557,135:0,-23,/3:88X,135:0,-23,-/3:183,135:0,-23,/3:216,135:0,-23,-/3 !\_9 ,8;"3-4";9 ,23;"3 -4";10 ,2;" =";10 ,18;" =";11 ,7;"-5 6";11 ,23;"5 -6":557,103g:0,-23,/3:88X,103g:0,-23,-/3:183,103g:0,-23,/3:216,103g:0,-23,-/3: !]""8541]! !^+5:0:="N"Ŧ="n"8560p! !_"S"Ʀ"s"8541]! !`7.1}L,35#:65001,22:65000 !a8710":8715 ":.1}L,35#:13 ,2;" Multiplicando por 2 0";15,25;"0 2";15,0;"traslada P a P(6,8),"''"ya que,";16,11 ;"2 0 3 6";18,11 ;"0 2 4 8";17,18;"=":199,71G:0,-23,/3:224,71G:0,-23,-/3:87W,47/:0,-23,/3:112p,47/:0,-23,-/3:127,47/:0,-23,/3:137,47/:0,-23,-/3:159,47/:0,-23,/3:168,47/:0,-23,-/3 !b19,0;"(aumento factor 2)":.1}L,35#::2,24;"(6,8) P":189,93]:45-,63?:190,93]:45-,63?:-7,-2:7,1:-2,-6:3,7 !cW8990#:65001,22:65000:8710":8715 ":.1}L,35#:13 ,3;"Multiplicando por -1 0";15,24;" 0 1":191,71G:0,-23,/3:224,71G:0,-23,-/3:16,0;"traslada P a P(-3,4)"''"(reflexion respecto al eje Y)" !d502:.1}L,35#:4,16;"P";5,15;"(-3,4)":188,91[:-23,32 :187,91[:-23,32 :2,-6:-2,7:6,-2:8990# !e65001,22:65000:8710":8715 ":.1}L,35#:13 ,2;"Multiplicando por 0 -1";15,24;"1 0":191,71G:0,-23,/3:224,71G:0,-23,-/3:16,0;"traslada P a P(-4,3)"'"(rotacion sobre el origen, de +90 grados en sentido contrario a las agujas del reloj). " !f502:.1}L,35#:5,18;"P";6,15;"(-4,3)":188,91[:-31,24:187,91[:-31,24:2,-6:-2,7:6,-2:8990# !g65001,22:65000:8710":.1}L,35#:6,26;1;"X";0;13 ,2;"La suma de la matriz 2";15,24;"-1":191,71G:0,-23,/3:208,71G:0,-23,-/3:15,0;"traslada P a P(5,3)"'"(traslada 2 unidades paralelas al eje X, y luego 1 unidad paralela al eje Y, en sentido negati- vo). " !h44,26;"P";5,25;"(3,4)":8990#:1:6,27;"X":1,35#:6,28;"X";6,27;"X":1,35#:7,28;"X";6,28;"X":502:0:8,28;"P";9 ,26;"(5,3)":8990# !i65001,22:65000:8710":.1}L,35#:13 ,0;" Podemos combinar muchas trans- formaciones de estas.Por ejemplola imagen (x,y) de un punto (x,y) nos la da la anterior transformacion:-;":8718" !j8990#:65001,11 :65000:11 ,0;"La imagen de";13 ,6;"2 0 1 2 3 4";15,6;"1 1 0 1 1 3";14,8;"es";14,18;"+";14,22;"=":8720":9 ,25;"X":8722":8990#:1,35#:8,24;"X":60<:1,35#:7,27;"X":8990# !k65001,22:65000:8710":8718":11 ,0;"La imagen de";13 ,6;"3 0 1 3 3 3";15,6;"0 1 0 0 1 4";14,8;"es";14,18;"+";14,22;"=":8720":10 ,26;"X":8722":8990#:1,35#:7,23;"X":60<:1,35#:6,26;"X":8990# !l65001,22:65000:8710":8718":11 ,0;"La imagen de";13 ,6;"0 0 1 0 3 5";15,6;"2 1 0 2 1 1";14,8;"es";14,18;"+";14,22;"=":8720":8,23;"X":8722":8990#:1,35#:10 ,25;"X":60<:1,35#:9 ,28;"X":8990# !m 8995## !n+5:0:="S"Ŧ="s"8544`! !o"N"Ʀ"n"8558n! !p65001,22:65000:1,35#:5,0;" Dibuja cuidadosamente diagramaspara resolver las preguntas si- guientes, sobre la transforma-- cion de matrices.":8990#:65001,19:65000:1,35#:4,0;"1.";4,21;"0.8 -0.6";6,21;"0.6 0.8":167,143:0,-23,/3:232,143:0,-23,-/3: !q""8561q! !r+5:0:="N"Ŧ="n"8577! !s"S"Ʀ"s"8561q! !t7.1}L,35#:65001,21:65000 !u|4,0;" La matriz troca en";3,11 ;"a b";3,21;"1";3,28;"a";5,11 ;"c d";5,21;"0";5,28;"c":87W,151:8750.":113q,151:8751/":167,151:8750.":176,151:8751/":223,151:8750.":232,151:8751/" !vF8,0;"ya que";7,7;"ab 1 a";8,14;"=";9 ,7;"cd 0 c";8,10 ;"X":557,119w:8750.":72H,119w:8751/":95_,119w:8750.":104h,119w:8751/":127,119w:8750.":136,119w:8751/" !w12 ,0;"y troca en .";11 ,10 ;"0 b";13 ,10 ;"1 d":79O,87W:8750.":88X,87W:8751/":135,87W:8750.":144,87W:8751/":8990# !x515,0;" Si conocemos las imagenes de";16,1;"1 0";18,1;"0 1";17,3;" y ,podemos escribir la"''"matriz de la transformacion.":7,47/:8750.":16,47/:8751/":557,47/:8750.":64@,47/:8751/" !y8990#:65001,21:65000:8740$":3,30;"X";3,20;"X";4,0;"ej. Halla la matriz"'"que transforma";6,1;"1 1"'" en y"'" 0 1"''" 0 -1"'" en"'" 1 1":7,127:8750.":16,127:8751/":63?,127:8750.":72H,127:8751/":7,95_:8750.":16,95_:8751/":63?,95_:8750.":80P,95_:8751/":8990#:14,0;" La matriz 1 -1"''"pedida es, 1 1":111o,63?:8750.":152,63?:8751/":17,0;" Esto representa un aumento con un factor de 2 y una rotacion de +45 grados. ":8990# !z244,108l:-12 ,28,/4:.1}L,35#:12 ,12 :3,30;"X":8990# !{204,148:-28,-12 ,/4:.1}L,35#:-12 ,12 :3,20;"X":8990# !}Z65000:3,0;" Matrices de la forma a b";5,23;"-b a"'"describen rotaciones."'''" Y las de la forma a b";11 ,23;"b -a"'"describen reflexiones.":183,151:8750.":216,151:8751/":183,103g:8750.":216,103g:8751/":8995## !~""8574~! !+5:0:="S"Ŧ="s"8564t! !"N"Ʀ"n"8574~! !.1}L,35#:65001,8:65000:16,0;" Dibuja diagramas para responderlas siguientes preguntas.":8990# !65001,21:65000:1,35#:4,0;"1."'" Halla la matriz que transforma"''" 1 0 0 -1"'" en y en"'" 0 -1 1 0":15,119w:8750.":24,119w:8751/":71G,119w:8750.":88X,119w:8751/":159,119w:8750.":168,119w:8751/":215,119w:8750.":232,119w:8751/": !0192,160:-88X,-64@:144,0:-568,64@:0,-64@:8,0:0,8:-8,0:135,96`:-8,15,/4:1;1,23;"B";10 ,12 ;"A";10 ,31;"C";10 ,23;"X": "i=124|2528:i,89Y:0,67C:i:i=92\1568:124|,i:128,0:i:124|,91[:128,0:187,89Y:0,67C:i=082:1;11 ,23+i;i:i:i=-8-22:1;11 ,22+i;i:i:i=282:1;10 -i,22;i:i:11 ,30;"x";2,21;"y": " 7,26;"P(3,4)":189,93]:22,31:190,93]:22,31:-7,-2:7,1:-2,-6:3,7:3,0;" =";2,7;"3";4,7;"4"'"indica la"'"posicion vector"'"del punto P"'"respecto del"'"origen.":557,159:0,-23,/3:64@,159:0,-23,-/3: "4,1;"x 0 1 x 3";6,1;"y 1 0 y 1";5,12 ;"+";5,3;"=":7,143:0,-23,/3:20,143:0,-23,-/3:39',143:0,-23,/3:65A,143:0,-23,-/3:79O,143:0,-23,/3:88X,143:0,-23,-/3:111o,143:0,-23,/3:120x,143:0,-23,-/3: "43+,71G:0,-23,/3:60<,71G:0,-23,-/3:87W,71G:0,-23,/3:112p,71G:0,-23,-/3:127,71G:0,-23,/3:137,71G:0,-23,-/3:159,71G:0,-23,/3:168,71G:0,-23,-/3:191,71G:0,-23,/3:200,71G:0,-23,-/3: "17,0;" La transformacion es una refle-xion respecto a la linea x-y=0, seguida de una translacion.":188,92\:64@,64@: "i=92\2528:i,12 :0,144:i:i=12 1568:92\,i:160,0:i:92\,77M:160,0:173,12 :0,144:1:i=05:12 -2*i,20;i;13 ,21+2*i;i:i:i=-5-12:13 ,20+2*i;i:i:i=-4-1:12 -2*i,19;i:i:0:13 ,30;"x";3,20;"y": "$i=1642448:i,68D:0,80P:i:205,68D:0,80P:i=68D1488:164,i:80P,0:i:164,109m:80P,0:9 ,31;"x";3,23;"y";1;9 ,19;"-1";9 ,24;"0";9 ,30;"1";13 ,23;"-1";3,24;"1";8,30;"X";3,25;"X": ".0,-23,/4: "/ 0,-23,-/4: #""8990# #p30:20,0;" Pulsa ENTER para continuar. ":2:0:="@"900 # T.1}L,35#:9 ;20,0;" ": ##17,0;" Deseas repasar otra vez antes de responder las preguntas? Pulsa S/N. ": #':.1}L,35#:7,0;" Para usar el modulo de nuevo, pulsa R Pulsa S para STOP ":9100# #("MODULO F"2 #)$"mat code 6"65000,600X # #""9100# #*5:0:="R"Ŧ="r"900 #"="S"Ŧ="s".5,20: # 9100# ttmptB ub. La imagen de (5) ( 4) ( )=( ) (0) ( ) u0.6x5+0.8x0 =3  Q 29I ra iiiii i~Ḻiiii1i1 i1 ͱi1i13333i1s333i1i1 i1ffffi1}L̶vax ylsinicctjG3UHVAmat code 6X€MZ D!X6(#!Y6(#!Y6(#!Z6(#!Y60#!Y60#!Y60#!Y60#!Z60#!0Z60#!PZ60#!pZ60#!Z60#!Z60#!Z60#!Z60# P P P 88 MMbXaXL8Wq !v>