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 Dilation Scale Factor

Compare the size of polygon \(ABCD\) and \(A'B'C'D'\). \(A'B'C'D'\) is smaller, so dilation scale factor is less than 1.

Step2: Analyze Transformation After Dilation

Check orientation: both polygons have the same orientation (no reflection, as reflection would flip orientation). So after dilation (scale <1), a translation occurs (no reflection, just moving).

Answer:

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