Question

triangle xyz was dilated using the rule ( d_{0,0.25}(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 \(Z'\) are \((-2,-1)\)

Step2: Use the dilation rule to find the pre - image coordinates

The dilation rule is \((x,y)\to(0.25x,0.25y)\). Let the coordinates of \(Z\) be \((a,b)\). Then \(0.25a=-2\) and \(0.25b = - 1\)

Step3: Solve for \(a\) and \(b\)

For \(a\):

$$
LATEXBLOCK0
$$

For \(b\):

$$
LATEXBLOCK1
$$

So the coordinates of \(Z\) (pre - image) are \((-8,-4)\)

Answer:

A. (-8, -4)