Question

identifying vertices of the pre - image of a dilation
triangle xyz was dilated using the rule ( d_{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,-4))
( (-8,2))
( (-2,-1))
( (-0.25,-0.5))

Explanation:

Step1: Determine the coordinates of \( Z' \)

From the graph, the coordinates of \( Z' \) (image) are \( (-2,-1) \).

Step2: Use the inverse of the dilation rule

The dilation rule is \( D_{0.25}(x,y)=(0.25x,0.25y) \). To find the pre - image, we use the inverse rule. If \( (x',y')=(0.25x,0.25y) \), then \( x = \frac{x'}{0.25}=4x' \) and \( y=\frac{y'}{0.25}=4y' \).
Substitute \( x'=-2 \) and \( y'=-1 \) into the inverse formulas:
\( x = 4\times(-2)=-8 \) and \( y = 4\times(-1)=-4 \)

Answer:

\((-8,-4)\)