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: \(ABCD\) and \(A'B'C'D'\) have the same orientation (no reflection, as reflection would flip orientation). So after dilation (scale <1), a translation occurs (to move the smaller polygon to the new position).

Step3: Eliminate Incorrect Options

• Reflection: Orientation same, so no reflection. Eliminate options with reflection.
• Scale factor >1: Image is smaller, so scale <1. Eliminate options with scale >1.

Answer:

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