Question

identifying vertices of the pre-image of a dilation
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?
$(-8, 2)$
$(-8, -4)$
$(-2, -1)$
$(-0.25, -0.5)$

Explanation:

Step1: Find coordinates of \( Z' \)

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

Step2: Apply dilation reverse rule

Dilation rule: \( (x, y) \to (0.25x, 0.25y) \). Let pre - image \( Z=(x,y) \), then \( 0.25x=-2 \), \( 0.25y = - 1 \).
Solve for \( x \): \( x=\frac{-2}{0.25}=-8 \).
Solve for \( y \): \( y=\frac{-1}{0.25}=-4 \).

Answer:

\((-8, - 4)\)