Question

which composition of similarity transformations would map polygon abdc to polygon abdc?
options:

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

Explanation:

Step1: Analyze Size Change

Compare the size of polygon \(ABDC\) and \(A'B'D'C'\). The image polygon \(A'B'D'C'\) is larger, so the scale factor of dilation is greater than 1.

Step2: Analyze Transformation Type

Check the orientation and position. The polygons seem to have a translation (shift) after dilation, not reflection or rotation (since orientation is similar, just shifted and enlarged). So the composition is a dilation with scale factor >1 and then a translation.

Answer:

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