Question

determining the similarity transformation

which composition of similarity transformations would map polygon abdc to polygon abdc?
○ a dilation with a scale factor greater than 1 and then a translation
○ a dilation with a scale factor greater than 1 and then a rotation
○ 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

Explanation:

Step1: Analyze Dilation Scale Factor

Compare the size of polygon \(ABDC\) and \(A'B'D'C'\). The image \(A'B'D'C'\) is larger than the original \(ABDC\), so the dilation scale factor must be greater than 1. This eliminates options with scale factor less than 1.

Step2: Analyze Transformation After Dilation

Check the orientation and position. The shapes have the same orientation (no reflection or rotation apparent), and after dilation (enlarging), a translation (shifting) would map \(ABDC\) to \(A'B'D'C'\). Rotation would change orientation, reflection would flip, but here it's a shift after enlargement.

Answer:

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