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

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

Step2: Analyze the orientation change

The orientation of the two polygons is different. A reflection (a flip) changes the orientation of a figure, while a translation (a slide) does not.

Answer:

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