Question

which composition of similarity transformations maps polygon abcd to polygon abcd? a dilation with a scale factor less than 1 and then a reflection a dilation with a scale factor less than 1 and then a translation a dilation with a scale factor greater than 1 and then a reflection a dilation with a scale factor greater than 1 and then a translation

Explanation:

Step1: Analyze the size change

The polygon \(A'B'C'D'\) is smaller than polygon \(ABCD\). A dilation with a scale factor less than \(1\) reduces the size of a figure.

Step2: Analyze the orientation change

The orientation of the two polygons (their left - right or up - down positions relative to each other) has changed. A reflection changes the orientation of a figure. A translation only moves a figure without changing its orientation, and a dilation with a scale factor greater than \(1\) would increase the size of the figure. So, the composition is a dilation with a scale factor less than \(1\) and then a reflection.

Answer:

a dilation with a scale factor less than 1 and then a reflection