Question

problem 10: spiral review
figure abcd is the image of figure abcd after a rotation around point e.
what is the length of side ab?
(image shows two figures: abcd (a pink polygon) and abcd (a rotated polygon) with ab labeled 9 and angle at d is 45°)

Explanation:

Step1: Recall Rotation Property

A rotation is a rigid transformation, so corresponding sides of the pre - image (ABCD) and image (A'B'C'D') are congruent.

Step2: Identify Corresponding Side

Side \( A'B' \) in the image corresponds to side \( AB \) in the pre - image. We know that the length of \( A'B' = 9 \).

Step3: Conclude Length of AB

Since \( AB\cong A'B' \) (by the property of rotation), the length of \( AB \) is equal to the length of \( A'B' \).

Answer:

9