Question

ms. romano draws figures a and a on the board.
a. are figures a and a similar? explain.
b. marcus says figure a is dilated to form figure a using a scale factor of 2 and point b as the center of dilation. what mistake did marcus make? what is the correct relationship?

Explanation:

Step1: Recall similarity definition

Two figures are similar if their corresponding angles are congruent and corresponding sides are in proportion. Since dilation is a transformation that produces similar figures, if figure A' is a dilation of figure A, they are similar.

Step2: Analyze dilation - scale factor error

If a figure is dilated from a center of dilation, the distance between each point in the original figure and the center of dilation is multiplied by the scale - factor to get the distance to the corresponding point in the dilated figure. If Marcus says the scale factor is 2, but the distances from point B (center of dilation) to corresponding points in A and A' do not have a ratio of 2, his error is in the stated scale factor. The correct scale factor can be found by comparing the distances of corresponding points from the center of dilation B.

Answer:

a. Yes, because a dilation produces similar figures.
b. Marcus may have mis - calculated the scale factor. To find the correct scale factor, measure the distances from the center of dilation B to corresponding points in A and A' and find their ratio.