Question

select all the pairs of polygons where the image appears to be the result of a dilation of the pre - image.

Explanation:

Step1: Recall the properties of dilation

Dilation is a transformation that changes the size of a figure but not its shape. The pre - image and the image are similar polygons.

Step2: Analyze each pair

• For the first pair: The inner pentagon and the outer pentagon have the same shape. The outer pentagon is larger than the inner pentagon, and they are centered in a way that suggests a dilation (same center of dilation conceptually).
• For the second pair: The shapes are not similar. The angles and side - length ratios do not match for a dilation.
• For the third pair: The shapes are not similar. The angles and side - length ratios do not match for a dilation.
• For the fourth pair: The inner quadrilateral and the outer polygon (a pentagon) are not of the same shape. So, no dilation.

Answer:

The first pair of polygons.