Question

similar figures
which composition of similarity transformations maps polygon abcd to polygon abcd?
a dilation with a scale factor of \\(\frac{1}{4}\\) and then a rotation
a dilation with a scale factor of 4 and then a translation
a dilation with a scale factor of \\(\frac{1}{4}\\) and then a translation
a dilation with a scale factor of 4 and then a rotation

Explanation:

Step1: Analyze Size Relationship

Polygon \(ABCD\) is larger than \(A'B'C'D'\), so the scale factor of dilation should be less than 1. So scale factor \(\frac{1}{4}\) (not 4) is correct, eliminating options with scale factor 4.

Step2: Analyze Transformation Type

After dilation, the orientation of \(A'B'C'D'\) relative to \(ABCD\) suggests a translation (no rotation needed as the shape's orientation doesn't change drastically; a translation can move the dilated figure to the position of \(A'B'C'D'\)). So dilation with scale factor \(\frac{1}{4}\) then translation.

Answer:

a dilation with a scale factor of \(\frac{1}{4}\) and then a translation