Question

kanisha drew pentagon a on a coordinate grid. she then performed a rotation followed by a dilation with scale factor 5 to produce pentagon b. which is a true statement about the two pentagons?
a. they are similar, but not congruent.
b. they are neither congruent nor similar.
c. they are similar and congruent.
d. they are congruent, but not similar.

Explanation:

Step1: Recall transformation properties

Rotation is a rigid - motion transformation (preserves shape and size). Dilation is a non - rigid transformation. If a figure is rotated (rigid - motion) and then dilated (non - rigid with scale factor \(k
eq1\)), the two figures (pre - image and image) are similar.
Since the scale factor is \(k = 5
eq1\), the two pentagons are not congruent (congruent figures have a scale factor of \(k = 1\) in dilation).

Answer:

A. They are similar, but not congruent.