On a coordinate plane, 2 polygons are shown. Polygon A B C D is larger than polygon A prime B prime C prime D prime and is reflected across the y-axis to form polygon A prime B prime C prime D prime.

Question

Which composition of similarity transformations maps polygon ABCD to polygon A'B'C'D'?

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

Answer 1

To determine the composition of similarity transformations that maps polygon ABCD to polygon A'B'C'D', we first note two key transformations that are involved:

1. Dilation: A dilation with a scale factor less than 1 will reduce the size of the polygon (from ABCD to A'B'C'D').
2. Reflection: Since the problem states that polygon ABCD is reflected across the y-axis to create polygon A'B'C'D', we need to account for this as well.

Given this:

• The fact that polygon A'B'C'D' is smaller than polygon ABCD implies that a dilation with a scale factor less than 1 is needed.
• Since the transformation involves reflecting across the y-axis, the composition must include a reflection.

Therefore, the correct answer to the composition of similarity transformations that maps polygon ABCD to polygon A'B'C'D' is:

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