Question

The dashed triangle is the image of the solid triangle. The center of dilation is (6, 6) .

Answer 1

The preimage is the solid triangle while the image is the dashed triangle. Recall that any transformation takes a preimage and maps it to an image. The "preimage" is the "before"; while the "image" is the "after"

Preimage ---> Image

Before ---> After

The "pre" is one way to help remember it means "before".

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The preimage has a horizontal segment length of 15 units (count from x=-9 to x=6 and you should count out 15 spaces). The corresponding horizontal piece on the dashed triangle is only 3 units long. Divide the image length over the preimage length

(image length)/(preimage length) = 3/15 = 1/5 = 0.2

Now if the figure wasn't reflected over the point (6,6), then the final answer would be either 1/5 or 0.2; however, this reflection does happen so we need to make the scale factor negative. So we go from 1/5 to -1/5, and we go from 0.2 to -0.2

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Final Answer as a fraction: -1/5

Final Answer in decimal form: -0.2