jueves, 28 de enero de 2010

HOMOTECIAS


Las homotecias transforman una figura plana en otra figura de igual forma, pero de menor o mayor tamaño, según el valor de la razón, k. Si k es positivo la homotecia es directa, y si no, es inversa. 


- Propiedades de las homotecias

1.o Toda recta que pasa por el centro de homotecia es invariante, es decir, se transforma en sí misma. . . 2.o Toda recta que no pasa por el centro de homotecia se transforma en otra recta paralela a la dada. 3.o La razón de dos segmentos homotéticos es...


Homotecia directa y homotecia inversa

En una homotecia de centro el punto O y razón k:


  • Si k > 0, A y A′ están al mismo lado de O, y se dice que la homotecia es directa.
  • Si k < 0, A y A′ están a distinto lado de O, y se dice que la homotecia es inversa.
A la figura ABCD le hemos aplicado una homotecia de centro O y razón k, con k > 0; homotecia directa.
A la figura ABC le hemos aplicado una homotecia de centro O y razón k, con k < 0; homotecia inversa.


 HOMOTECIA DIRECTA


HOMOTECIA INVERSA

Propiedades de las homotecias

1.o Toda recta que pasa por el centro de homotecia es invariante, es decir, se transforma en sí misma.

 

HOMOTECIA RECTA

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  1. 2.o Toda recta que no pasa por el centro de homotecia se transforma en otra recta paralela a la dada.
  2. 3.o La razón de dos segmentos homotéticos es igual a la razón k de la homotecia.
 

SEGMENTOS HOMOTETICOS
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4.o Una homotecia transforma los ángulos en ángulos iguales.
 


ANGULOS HOMOTETICOS
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Homotecia: amplificacion o reduccion geometrica que tiene la finalidad de amplificar o reducir una figura para poder darle usos diversos.

Caracteristicas:
1.- medidad proporcionales
2.-son semejantes
3.-angulos iguales
4.-son a escala

Tipos de homotecia:
1.-HOMOTECIA DIRECTA: es aquella en la cual el punto de homotecia o el centro de homotecia se encuantra despues o antes de la figura trazada. La caracteriztica principal es que los segmentos entre las figuras son paralelas.

2.-HOMOTECIA INVERSA: Es aquella en la cual el centro de homotecia se encuentra entre la figura.

La homotecia tambien puede ser positiva o negativa. Determinan la razon que se tome es decir, el factor principal por el cual se multiplica.
Para encontrar la razon de homotecia debe colocarse uno a uno cada lado o segmento de las figuras y sacar la constante de proporcionalidad.


Sea k un número positivo, cuando aplicamos una homotecia de centro O y razón k a un punto cualquiera P, obtenemos otro punto P' de la semirrecta que definen O y P, de manera que
Al punto P' lo denominaremos homólogo de P.

Ten en cuenta que si k<1, el punto P' queda situado entre O y P.


También se pueden considerar homotecias en la que la razón sea negativa, en la  figura tienes el efecto de aplicar una homotecia de centro O y razón -2 al Triángulo ABC:

 Cuando la razón es negativa, el centro de la homotecia queda situado entre el punto y su imagen.

 

44 comentarios:

Unknown dijo...

Que Es Homotecia Positiva y Negativa?? :D

Unknown dijo...
Este comentario ha sido eliminado por el autor.
Unknown dijo...

Muy bueno ....gracias.....ñ.ñ......emm pero lo único k no entendí fue la 3°propiedad .-.

Unknown dijo...

¿Porqué pasa la homotecia?

Alejandro Gaete dijo...

Para entender la Homotecia

Unknown dijo...

Tengo un ejercici y dice hallar el valor de k en las sigtes Homotecias de manera que el segundo punto sea imagen el primero:

[8,-8 -> 16, -16] Me urge el trabajo es para hoy

Unknown dijo...

Tengo un ejercici y dice hallar el valor de k en las sigtes Homotecias de manera que el segundo punto sea imagen el primero:

[8,-8 -> 16, -16] Me urge el trabajo es para hoy

Unknown dijo...
Este comentario ha sido eliminado por el autor.
Francisco Pizarro dijo...

Tengo un ejercici y dice hallar el valor de k en las sigtes Homotecias de manera que el segundo punto sea imagen el primero:

[8,-8 -> 16, -16] Me urge el trabajo es para hoy
EN ESE CASO LA HOMOTECIA TENDRIA UN VALOR DE K=2 [8xk,-8xk=16, -16]

Unknown dijo...
Este comentario ha sido eliminado por el autor.
Unknown dijo...
Este comentario ha sido eliminado por el autor.
Unknown dijo...

Mientras mas grande sea la razon de homotecia, mas grande sera, aunque sea negativo?; como por ejemplo un -3 comparado con un -1.

Unknown dijo...

el profe me pidio que hiciera un trabajo con "criterios de semejanza de la homotecia" y la verdad he buscado por todo internet y no me saLE NADITA aiudaaa :(

Unknown dijo...

No entendí nada :"D

Unknown dijo...

Excellent post !!!. The strategy you have posted on this technology helped me get into
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Nice post.
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Unknown dijo...

Como hago cuando dice tres puntos alineados a,b,c y me piden que halle la razón de la homotecia que transforma b en c

Unknown dijo...

Que onda perros aqui aciendo la tarea toda aburrida.

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