Question

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

What is the scale factor used to create the dilation? Enter your answer as an integer or decimal in the box.

Answer 1

The scale factor used to create the dilation is sqrt(72) / 6.

Step-by-step explanation:

In order to find the scale factor used to create the dilation, we need to compare the corresponding side lengths of the solid triangle and dashed triangle. Since the center of dilation is (6, 6), we can calculate the distance between the center and any vertex of the solid triangle using the distance formula.

Let's choose a convenient vertex, such as (0, 0). The distance between (0, 0) and (6, 6) is:

d = sqrt((6 - 0)2 + (6 - 0)2) = sqrt(36 + 36) = sqrt(72).

Since the dashed triangle is the image of the solid triangle, the corresponding side lengths are proportional. Therefore, the scale factor is the ratio of the corresponding side lengths:

Scale factor = Length of a side of the dashed triangle / Length of the corresponding side of the solid triangle = sqrt(72) / 6.

Answer 2

-0.2

Step-by-step explanation:

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