The composition of similarity transformations maps polygon ABCD to polygon A'B'C'D' is a dilation with a scale factor of  and then a translation. Option (b) is correct.
 and then a translation. Option (b) is correct.
Further explanation:
The rule of transformation of the coordinates can be expressed as follows,

Here, k represents the scale factor.
Given:
The options are as follows,
(a). A dilation with a scale factor of  and then a rotation
 and then a rotation
(b). A dilation with a scale factor of  and then a translation
 and then a translation
(c). A dilation with a scale factor of 4 and then a rotation.
(d). A dilation with a scale factor of 4 and then a translation
Explanation:
The length of side  is
 is  of side AB.
 of side AB.
The length of side  is
 is  of side AD.
 of side AD.
The length of side  is
 is  of side DB.
 of side DB.
The length of side  is
 is  of side CB.
 of side CB.
The composition of similarity transformations maps polygon ABCD to polygon A'B'C'D' is a dilation with a scale factor of  and then a translation. Option (b) is correct.
 and then a translation. Option (b) is correct.
Learn more:
- Learn more about inverse of the functionhttps://brainly.com/question/1632445.
- Learn more about equation of circle brainly.com/question/1506955.
-  Learn more about range and domain of the function brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Coordinate geometry
Keywords: composition, image vertices, dilation, center, scale factor, four, coordinates, x-coordinates, y-coordinate, transformation rule,