Question

triangle xyz was dilated using the rule $d_{o,0.25} (x, y) \to (0.25x, 0.25y)$. the image is shown in the diagram. what are the coordinates of z of the pre-image? $\bigcirc (-8, -4)$ $\bigcirc (-8, 2)$ $\bigcirc (-2, -1)$ $\bigcirc (-0.25, -0.5)$

Explanation:

Step1: Find coordinates of \( Z' \)

From the diagram, \( Z' \) has coordinates \( (-2, -1) \).

Step2: Apply dilation inverse formula

Dilation rule: \( (x, y) \to (0.25x, 0.25y) \). Let pre - image \( Z=(x,y) \), then \( 0.25x=-2 \) and \( 0.25y = - 1 \).

Solve for \( x \): \( x=\frac{-2}{0.25}=-8 \)

Solve for \( y \): \( y=\frac{-1}{0.25}=-4 \)

Answer:

\( (-8, -4) \)