Question

On a coordinate plane, which single transformation could map point A (3,-4) onto point A' (1.5,-2)? *

Answer 1

Answer: A dilation with rule: $(x,y)\to(\dfrac12x,\dfrac12y)$

Explanation:

A dilation is a non-rigid transformation that creates an image that is the same shape as the original but has a different size.

It uses a scale factor k such that

$(x,y)\to(kx,ky)$

(x,y)= coordinates of original figure

(kx,ky) = corresponding coordinate in the image.

To transform: A (3,-4) onto point A' (1.5,-2).

Using scale factor k= $\dfrac12$, we have

$A(3,-4)\to A'(\dfrac12\times3, \dfrac12\times-4)=A'(1.5,-2)$

Required rule: $(x,y)\to(\dfrac12x,\dfrac12y)$