Question

which description of a figure and its image match the transformation described by $(x,y)\to(x,3y)$?
a the figure and its image are similar and the image has been translated 3 units up.
b the figure and its image are similar and the image has been translated 3 units to the right.
c the figure and its image are neither similar nor congruent, and the image has been stretched horizontally.
d the figure and its image are neither similar nor congruent, and the image has been stretched vertically.

Explanation:

Step1: Analizar la transformación

La transformación \((x,y)\to(x,3y)\) multiplica la coordenada \(y\) por \(3\). Esto significa que la figura se estira verticalmente.

Step2: Verificar la similitud y congruencia

Como se estira la figura (cambia la longitud en una dirección), no es congruente. Y como no se mantiene la proporción en todas las direcciones (solo se modifica \(y\)), no es similar.

Answer:

D. The figure and its image are neither similar nor congruent, and the image has been stretched vertically.