Question

triangle xyz was dilated using the rule ( d_{o,0.25}(x,y)
ightarrow(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 \( Z' \) are \( (-2,-1) \).

Step2: Use the inverse of the dilation rule

The dilation rule is \( D_{O,0.25}(x,y)\to(0.25x,0.25y) \). To find the pre - image, we use the inverse rule \( (x,y)\to(4x,4y) \) (since \( \frac{1}{0.25}=4 \)).
For \( Z'(-2,-1) \), the \( x \) - coordinate of the pre - image \( Z \) is \( 4\times(-2)=-8 \) and the \( y \) - coordinate is \( 4\times(-1)=-4 \).

Answer:

\((-8, -4)\)