LA RECTA DE EULER physicsleninac@hotmail.comJSFH INGRESE LAS COORDENADAS DE LOS PUNTOS A, B Y C A = ( , ) B = ( , ) C = ( , ) use DocumentTools in trian:=Do([[%x1,%y1], [%x2,%y2], [%x3,%y3]]): lp:=Do(polygonplot(trian,axes=boxed,color="DarkGreen",transparency=.5)): Do(point(A,%x1,%y1)): Do(point(B,%x2,%y2)): Do(point(C,%x3,%y3)): line(l1,[A,B]): line(l2,[A,C]): line(l3,[B,C]): eq1:=Equation(l1,[x,y]); eq2:=Equation(l2,[x,y]); eq3:=Equation(l3,[x,y]); g1:=plot(solve(eq1,y),x=-10..10,y=-10..10,color="DarkGreen",transparency=1.0); g2:=plot(solve(eq2,y),x=-10..10,y=-10..10,color="DarkGreen",transparency=1.0); g3:=plot(solve(eq3,y),x=-10..10,y=-10..10,color="DarkGreen",transparency=1.0); ##### HALLANDO LA EC. DE LAS MEDIANAS ########## midpoint(AB,A,B),midpoint(AC,A,C),midpoint(BC,B,C): line(mediana1,[A,BC]),line(mediana2,[B,AC]),line(mediana3,[C,AB]): eq4:=Equation(mediana1,[x,y]); eq5:=Equation(mediana2,[x,y]); eq6:=Equation(mediana3,[x,y]); g4:=plot(solve(eq4,y),x=-10..10,y=-10..10): g5:=plot(solve(eq5,y),x=-10..10,y=-10..10): g6:=plot(solve(eq6,y),x=-10..10,y=-10..10): interseccion_medianas:=solve({eq5,eq6},{x,y}): pxintm:=eval(x,interseccion_medianas): pyintm:=eval(y,interseccion_medianas): point(IM,pxintm,pyintm): ######## GRAFICANDO LOS PUNTOS NOTABLES ################ ptsnot:=pointplot(Matrix([[pxintm,pyintm]],datatype=float),axes=normal,color=blue,symbol=asterisk,symbolsize=40): glA:=Do(textplot([%x1,%y1, "A"],'align'={'above','right'})); glB:=Do(textplot([%x2,%y2, "B"],'align'={'above','right'})); glC:=Do(textplot([%x3,%y3, "C"],'align'={'above','right'})); gbar:=Do(textplot([pxintm,pyintm,"Bar"],'align'={'above','right'},'color'="Red")); ######### SALIDA ################# Do(%GREULR=display(lp,g1,g2,g3,g4,g5,g6,ptsnot,glA,glB,glC,gbar,gridlines=true,view=[-10..10,-10..10])); ########## CALCULO DE ECUACIONES ###################### Do(%meduno=eq4); Do(%meddos=eq5); Do(%medtres=eq6); Do(%coordbar=interseccion_medianas); Do(%rsnbar=evalf(interseccion_medianas,5)); ########## OTROS CALCULOS ########## Do(triangle(abc,[point(a,%x1,%y1),point(b,%x2,%y2),point(c,%x3,%y3)])); Do(%artr=area(abc)); Do(%areanum=evalf(%artr,5)); Do(%distAB=distance(a,b)); Do(%distAC=distance(a,c)); Do(%distBC=distance(b,c)); Do(%perim=evalf(%distAB+%distAC+%distBC,5)); Do(%eclAB=eq1); Do(%eclAC=eq2); Do(%eclBC=eq3); #########RESET########## Do(%altuno=NULL): Do(%altdos=NULL): Do(%alttres=NULL): Do(%coordort=NULL): Do(%vnorto=NULL): Do(%medtzuno=NULL): Do(%medtzdos=NULL): Do(%medtztres=NULL): Do(%coordmdz=NULL): Do(%vnmdz=NULL): Do(%eceulr=NULL): end use; use DocumentTools in trian:=Do([[%x1,%y1], [%x2,%y2], [%x3,%y3]]): lp:=Do(polygonplot(trian,axes=boxed,color="DarkGreen",transparency=.5)): Do(point(A,%x1,%y1)): Do(point(B,%x2,%y2)): Do(point(C,%x3,%y3)): line(l1,[A,B]): line(l2,[A,C]): line(l3,[B,C]): eq1:=Equation(l1, [x, y]); eq2:=Equation(l2, [x, y]); eq3:=Equation(l3, [x, y]); g1:=plot(solve(eq1,y),x=-10..10,y=-10..10,color="DarkGreen",transparency=1.0); g2:=plot(solve(eq2,y),x=-10..10,y=-10..10,color="DarkGreen",transparency=1.0); g3:=plot(solve(eq3,y),x=-10..10,y=-10..10,color="DarkGreen",transparency=1.0); ##### HALLANDO LA EC. DE LAS ALTURAS ########## altura1:=PerpendicularLine(la1,A,l3); altura2:=PerpendicularLine(la2,B,l2); altura3:=PerpendicularLine(la3,C,l1); eq7:=Equation(altura1,[x,y]); eq8:=Equation(altura2,[x,y]); eq9:=Equation(altura3,[x,y]); g7:=plot(solve(eq7,y),x=-10..10,y=-10..10,color="MediumBlue"); g8:=plot(solve(eq8,y),x=-10..10,y=-10..10,color="MediumBlue"); g9:=plot(solve(eq9,y),x=-10..10,y=-10..10,color="MediumBlue"); interseccion_alturas:=solve({eq8,eq9},{x,y}): pxinta:=eval(x,interseccion_alturas): pyinta:=eval(y,interseccion_alturas): point(IA,pxinta,pyinta): ######## GRAFICANDO LOS PUNTOS NOTABLES ################ ptsnot:=pointplot(Matrix([[pxinta,pyinta]],datatype=float),axes=normal,color=blue,symbol=asterisk,symbolsize=40): glA:=Do(textplot([%x1,%y1, "A"],'align'={'above','right'})); glB:=Do(textplot([%x2,%y2, "B"],'align'={'above','right'})); glC:=Do(textplot([%x3,%y3, "C"],'align'={'above','right'})); gort:=Do(textplot([pxinta,pyinta,"Ort"],'align'={'above','right'},'color'="Blue")); ######### SALIDA ################# Do(%GREULR=display(lp,g1,g2,g3,g7,g8,g9,ptsnot,glA,glB,glC,gort,gridlines=true, view=[-10..10,-10..10])); ########## CALCULO DE ECUACIONES ###################### Do(%altuno=eq7); Do(%altdos=eq8); Do(%alttres=eq9); Do(%coordort=interseccion_alturas); Do(%vnorto=evalf(interseccion_alturas,5)); ########## OTROS CALCULOS ########## Do(triangle(abc,[point(a,%x1,%y1),point(b,%x2,%y2),point(c,%x3,%y3)])); Do(%artr=area(abc)); Do(%areanum=evalf(%artr,5)); Do(%distAB=distance(a,b)); Do(%distAC=distance(a,c)); Do(%distBC=distance(b,c)); Do(%perim=evalf(%distAB+%distAC+%distBC,5)); Do(%eclAB=eq1); Do(%eclAC=eq2); Do(%eclBC=eq3); #########RESET########## Do(%meduno=NULL): Do(%meddos=NULL): Do(%medtres=NULL): Do(%coordbar=NULL): Do(%rsnbar=NULL): Do(%medtzuno=NULL): Do(%medtzdos=NULL): Do(%medtztres=NULL): Do(%coordmdz=NULL): Do(%vnmdz=NULL): Do(%eceulr=NULL): end use; use DocumentTools in trian:=Do([[%x1,%y1], [%x2,%y2], [%x3,%y3]]): lp:=Do(polygonplot(trian,axes=boxed,color="DarkGreen",transparency=.5)): Do(point(A,%x1,%y1)): Do(point(B,%x2,%y2)): Do(point(C,%x3,%y3)): line(l1,[A,B]): line(l2,[A,C]): line(l3,[B,C]): eq1:=Equation(l1, [x, y]); eq2:=Equation(l2, [x, y]); eq3:=Equation(l3, [x, y]); g1:=plot(solve(eq1,y),x=-10..10,y=-10..10,color="DarkGreen",transparency=1.0); g2:=plot(solve(eq2,y),x=-10..10,y=-10..10,color="DarkGreen",transparency=1.0); g3:=plot(solve(eq3,y),x=-10..10,y=-10..10,color="DarkGreen",transparency=1.0); ##### HALLANDO LA EC. DE LAS MEDIATRICES ########## mediatriz1:=PerpendicularLine(lm1,AB,l1); mediatriz2:=PerpendicularLine(lm2,AC,l2); mediatriz3:=PerpendicularLine(lm3,BC,l3); eq10:=Equation(mediatriz1,[x,y]); eq11:=Equation(mediatriz2,[x,y]); eq12:=Equation(mediatriz3,[x,y]); g10:=plot(solve(eq10,y),x=-10..10,y=-10..10,color="OrangeRed"); g11:=plot(solve(eq11,y),x=-10..10,y=-10..10,color="OrangeRed"); g12:=plot(solve(eq12,y),x=-10..10,y=-10..10,color="OrangeRed"); interseccion_mediatrices:=solve({eq11,eq12},{x, y}): pxintmd:=eval(x,interseccion_mediatrices): pyintmd:=eval(y,interseccion_mediatrices): point(IMZ,pxintmd,pyintmd); ######## GRAFICANDO LOS PUNTOS NOTABLES ################ ptsnot:=pointplot(Matrix([[pxintmd,pyintmd]],datatype=float),axes=normal,color=blue,symbol=asterisk,symbolsize=40): glA:=Do(textplot([%x1,%y1, "A"],'align'={'above','right'})); glB:=Do(textplot([%x2,%y2, "B"],'align'={'above','right'})); glC:=Do(textplot([%x3,%y3, "C"],'align'={'above','right'})); gmdz:=Do(textplot([pxintmd,pyintmd,"Crc"],'align'={'above','right'},'color'="Orange")); ######### SALIDA ################# Do(%GREULR=display(lp,g1,g2,g3,g10,g11,g12,ptsnot,glA,glB,glC,gmdz,gridlines=true, view=[-10..10,-10..10])); ########## CALCULO DE ECUACIONES ###################### Do(%medtzuno=eq10); Do(%medtzdos=eq11); Do(%medtztres=eq12); Do(%coordmdz=interseccion_mediatrices); Do(%vnmdz=evalf(interseccion_mediatrices,5)); ########## OTROS CALCULOS ########## Do(triangle(abc,[point(a,%x1,%y1),point(b,%x2,%y2),point(c,%x3,%y3)])); Do(%artr=area(abc)); Do(%areanum=evalf(%artr,5)); Do(%distAB=distance(a,b)); Do(%distAC=distance(a,c)); Do(%distBC=distance(b,c)); Do(%perim=evalf(%distAB+%distAC+%distBC,5)); Do(%eclAB=eq1); Do(%eclAC=eq2); Do(%eclBC=eq3); #########RESET########## Do(%meduno=NULL): Do(%meddos=NULL): Do(%medtres=NULL): Do(%coordbar=NULL): Do(%rsnbar=NULL): Do(%altuno=NULL): Do(%altdos=NULL): Do(%alttres=NULL): Do(%coordort=NULL): Do(%vnorto=NULL): Do(%eceulr=NULL): end use; 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NiI= use DocumentTools in trian:=Do([[%x1,%y1], [%x2,%y2], [%x3,%y3]]): lp:=Do(polygonplot(trian,axes=boxed,color="DarkGreen",transparency=.5)): Do(point(A,%x1,%y1)): Do(point(B,%x2,%y2)): Do(point(C,%x3,%y3)): line(l1,[A,B]): line(l2,[A,C]): line(l3,[B,C]): eq1:=Equation(l1, [x, y]); eq2:=Equation(l2, [x, y]); eq3:=Equation(l3, [x, y]); g1:=plot(solve(eq1,y),x=-10..10,y=-10..10,color="DarkGreen",transparency=1.0); g2:=plot(solve(eq2,y),x=-10..10,y=-10..10,color="DarkGreen",transparency=1.0); g3:=plot(solve(eq3,y),x=-10..10,y=-10..10,color="DarkGreen",transparency=1.0); ##### HALLANDO LA EC. DE LAS MEDIANAS ########## midpoint(AB,A,B),midpoint(AC,A,C),midpoint(BC, B, C): line(mediana1,[A,BC]),line(mediana2,[B, AC]),line(mediana3,[C, AB]): eq4:=Equation(mediana1,[x,y]); eq5:=Equation(mediana2,[x,y]); eq6:=Equation(mediana3,[x,y]); g4:=plot(solve(eq4,y),x=-10..10,y=-10..10): g5:=plot(solve(eq5,y),x=-10..10,y=-10..10): g6:=plot(solve(eq6,y),x=-10..10,y=-10..10): interseccion_medianas:=solve({eq5,eq6},{x,y}): pxintm:=eval(x,interseccion_medianas): pyintm:=eval(y,interseccion_medianas): point(IM,pxintm,pyintm): ##### HALLANDO LA EC. DE LAS ALTURAS ########## altura1:=PerpendicularLine(la1,A,l3); altura2:=PerpendicularLine(la2,B,l2); altura3:=PerpendicularLine(la3,C,l1); eq7:=Equation(altura1,[x,y]); eq8:=Equation(altura2,[x,y]); eq9:=Equation(altura3,[x,y]); g7:=plot(solve(eq7,y),x=-10..10,y=-10..10,color="MediumBlue"); g8:=plot(solve(eq8,y),x=-10..10,y=-10..10,color="MediumBlue"); g9:=plot(solve(eq9,y),x=-10..10,y=-10..10,color="MediumBlue"); interseccion_alturas:=solve({eq8,eq9},{x,y}): pxinta:=eval(x,interseccion_alturas): pyinta:=eval(y,interseccion_alturas): point(IA,pxinta,pyinta): ##### HALLANDO LA EC. DE LAS MEDIATRICES ########## mediatriz1:=PerpendicularLine(lm1,AB,l1); mediatriz2:=PerpendicularLine(lm2,AC,l2); mediatriz3:=PerpendicularLine(lm3,BC,l3); eq10:=Equation(mediatriz1,[x,y]); eq11:=Equation(mediatriz2,[x,y]); eq12:=Equation(mediatriz3,[x,y]); g10:=plot(solve(eq10,y),x=-10..10,y=-10..10,color="OrangeRed"); g11:=plot(solve(eq11,y),x=-10..10,y=-10..10,color="OrangeRed"); g12:=plot(solve(eq12,y),x=-10..10,y=-10..10,color="OrangeRed"); interseccion_mediatrices:=solve({eq11,eq12},{x, y}): pxintmd:=eval(x,interseccion_mediatrices): pyintmd:=eval(y,interseccion_mediatrices): point(IMZ,pxintmd,pyintmd); ####### ECUACI\303\223N DE EULER ############### line(leu,[IM,IA]): eqeu:=Equation(leu,[x, y]); Do(%eceulr=simplify(eqeu)); geulr:=plot(solve(eqeu,y),x=-10..10,y=-10..10,color="LimeGreen"); ######## GRAFICANDO LOS PUNTOS NOTABLES ################ ptsnot:=pointplot(Matrix([[pxintm,pyintm],[pxinta,pyinta],[pxintmd,pyintmd]],datatype=float),axes=normal,color=blue,symbol=asterisk,symbolsize=40): glA:=Do(textplot([%x1,%y1, "A"],'align'={'above','right'})); glB:=Do(textplot([%x2,%y2, "B"],'align'={'above','right'})); glC:=Do(textplot([%x3,%y3, "C"],'align'={'above','right'})); gbar:=Do(textplot([pxintm,pyintm,"Bar"],'align'={'above','right'},'color'="Red")); gort:=Do(textplot([pxinta,pyinta,"Ort"],'align'={'above','right'},'color'="Blue")); gmdz:=Do(textplot([pxintmd,pyintmd,"Crc"],'align'={'above','right'},'color'="Orange")); ######### SALIDA ################# Do(%GREULR=display(lp,g1,g2,g3,g4,g5,g6,g7,g8,g9,g10,g11,g12,geulr,ptsnot,glA,glB,glC,gbar,gort,gmdz,gridlines=true, view=[-10..10,-10..10])); ########## CALCULO DE ECUACIONES ###################### Do(%meduno=eq4); Do(%meddos=eq5); Do(%medtres=eq6); Do(%coordbar=interseccion_medianas); Do(%rsnbar=evalf(interseccion_medianas,5)); Do(%altuno=eq7); Do(%altdos=eq8); Do(%alttres=eq9); Do(%coordort=interseccion_alturas); Do(%vnorto=evalf(interseccion_alturas,5)); Do(%medtzuno=eq10); Do(%medtzdos=eq11); Do(%medtztres=eq12); Do(%coordmdz=interseccion_mediatrices); Do(%vnmdz=evalf(interseccion_mediatrices,5)); ########## OTROS CALCULOS ########## Do(triangle(abc,[point(a,%x1,%y1),point(b,%x2,%y2),point(c,%x3,%y3)])); Do(%artr=area(abc)); Do(%areanum=evalf(%artr,5)); Do(%distAB=distance(a,b)); Do(%distAC=distance(a,c)); Do(%distBC=distance(b,c)); Do(%perim=evalf(%distAB+%distAC+%distBC,5)); Do(%eclAB=eq1); Do(%eclAC=eq2); Do(%eclBC=eq3); end use; use DocumentTools in Do(%x1=NULL): Do(%y1=NULL): Do(%x2=NULL): Do(%y2=NULL): Do(%x3=NULL): Do(%y3=NULL): Do(%altdos=NULL): Do(%alttres=NULL): Do(%altuno=NULL): Do(%areanum=NULL): Do(%artr=NULL): Do(%coordbar=NULL): DO(%coordmdz=NULL): Do(%coordort=NULL): Do(%distAB=NULL): Do(%distAC=NULL): Do(%distBC=NULL): Do(%eceulr=NULL): Do(%eclAB=NULL): Do(%eclAC=NULL): Do(%eclBC=NULL): Do(%meddos=NULL): Do(%medtres=NULL): Do(%medtzdos=NULL): Do(%medtztres=NULL): Do(%medtzuno=NULL): Do(%meduno=NULL): Do(%perim=NULL): Do(%rsnbar=NULL): Do(%vnmdz=NULL): Do(%vnorto=NULL): Do(%coordmdz=NULL): Do(%GREULR=plots[display](plots[textplot]([0,0,""]),axes=none)); end use; NOTA: 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 Ecuaciones de las Medianas ; ; Coordenadas del Baricentro: (Bar) = Ecuaciones de las Alturas ; ; Coordenadas del Ortocentro: (Ort) = Ecuaciones de las Mediatrices ; ; Coordenadas del Circuncentro: (Crc) = ECUACI\303\223N DE EULER: Recta que pasa por los puntos Bar. Ort. y Crc OTROS CALCULOS Area del Tri\303\241ngulo: = u^2 Distancia { AB = u , AC = u , BC = u } ---> Per\303\255metro = u Ecuaciones de las rectas de los lados del tri\303\241ngulo AB = , AC = , BC = use DocumentTools in trian:=Do([[%x1,%y1], [%x2,%y2], [%x3,%y3]]): lp:=Do(polygonplot(trian,axes=boxed,color="DarkGreen",transparency=.5)): Do(point(A,%x1,%y1)): Do(point(B,%x2,%y2)): Do(point(C,%x3,%y3)): line(l1,[A,B]): line(l2,[A,C]): line(l3,[B,C]): eq1:=Equation(l1, [x, y]); eq2:=Equation(l2, [x, y]); eq3:=Equation(l3, [x, y]); g1:=plot(solve(eq1,y),x=0..10,y=0..10,color="DarkGreen",transparency=1.0); g2:=plot(solve(eq2,y),x=0..10,y=0..10,color="DarkGreen",transparency=1.0); g3:=plot(solve(eq3,y),x=0..10,y=0..10,color="DarkGreen",transparency=1.0); ##### HALLANDO LA EC. DE LAS MEDIANAS ########## midpoint(AB,A,B),midpoint(AC,A,C),midpoint(BC, B, C): line(mediana1,[A,BC]),line(mediana2,[B, AC]),line(mediana3,[C, AB]): eq4:=Equation(mediana1,[x,y]); eq5:=Equation(mediana2,[x,y]); eq6:=Equation(mediana3,[x,y]); interseccion_medianas:=solve({eq5,eq6},{x,y}): pxintm:=eval(x,interseccion_medianas): pyintm:=eval(y,interseccion_medianas): point(IM,pxintm,pyintm): ##### HALLANDO LA EC. DE LAS ALTURAS ########## altura1:=PerpendicularLine(la1,A,l3); altura2:=PerpendicularLine(la2,B,l2); altura3:=PerpendicularLine(la3,C,l1); eq7:=Equation(altura1,[x,y]); eq8:=Equation(altura2,[x,y]); eq9:=Equation(altura3,[x,y]); interseccion_alturas:=solve({eq8,eq9},{x,y}): pxinta:=eval(x,interseccion_alturas): pyinta:=eval(y,interseccion_alturas): point(IA,pxinta,pyinta): ##### HALLANDO LA EC. DE LAS MEDIATRICES ########## mediatriz1:=PerpendicularLine(lm1,AB,l1); mediatriz2:=PerpendicularLine(lm2,AC,l2); mediatriz3:=PerpendicularLine(lm3,BC,l3); eq10:=Equation(mediatriz1,[x,y]); eq11:=Equation(mediatriz2,[x,y]); eq12:=Equation(mediatriz3,[x,y]); interseccion_mediatrices:=solve({eq11,eq12},{x, y}): pxintmd:=eval(x,interseccion_mediatrices): pyintmd:=eval(y,interseccion_mediatrices): point(IMZ,pxintmd,pyintmd); ####### ECUACI\303\223N DE EULER ############### line(leu,[IM,IA]): eqeu:=Equation(leu,[x, y]); Do(%eceulr=simplify(eqeu)); geulr:=plot(solve(eqeu,y),x=-10..10,y=-10..10,color="LimeGreen"); ######## GRAFICANDO LOS PUNTOS NOTABLES ################ ptsnot:=pointplot(Matrix([[pxintm,pyintm],[pxinta,pyinta],[pxintmd,pyintmd]],datatype=float),axes=normal,color=blue,symbol=asterisk,symbolsize=40): glA:=Do(textplot([%x1,%y1,"A"],'align'={'above','right'})); glB:=Do(textplot([%x2,%y2,"B"],'align'={'above','right'})); glC:=Do(textplot([%x3,%y3,"C"],'align'={'above','right'})); gbar:=Do(textplot([pxintm,pyintm,"Bar"],'align'={'above','right'},'color'="Red")); gort:=Do(textplot([pxinta,pyinta,"Ort"],'align'={'above','right'},'color'="Blue")); gmdz:=Do(textplot([pxintmd,pyintmd,"Crc"],'align'={'above','right'},'color'="Orange")); ######### SALIDA ################# Do(%GREULR=display(lp,g1,g2,g3,geulr,ptsnot,glA,glB,glC,gbar,gort,gmdz,gridlines=true, view=[-10..10,-10..10])); #########RESET########## Do(%meduno=NULL): Do(%meddos=NULL): Do(%medtres=NULL): Do(%coordbar=NULL): Do(%rsnbar=NULL): Do(%altuno=NULL): Do(%altdos=NULL): Do(%alttres=NULL): Do(%coordort=NULL): Do(%vnorto=NULL): Do(%medtzuno=NULL): Do(%medtzdos=NULL): Do(%medtztres=NULL): Do(%coordmdz=NULL): Do(%vnmdz=NULL): end use; Ejemplo: A(6,6) , B(-5,7) y C(0,-6) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=