Question

triangle trs is rotated about point x, resulting in triangle bac. figure may not be drawn to scale. if ab = 10 ft, ac = 14 ft, and bc = 20 ft, what is rs?
○ 10 ft
○ 14 ft
○ 20 ft
○ 24 ft

Explanation:

Step1: Recall Rotation Property

Rotation is a rigid transformation, so corresponding sides of the pre - image (△TRS) and image (△BAC) are congruent.

Step2: Identify Corresponding Sides

We need to find which side of △BAC corresponds to RS in △TRS. From the rotation, we can see that RS corresponds to AC (by looking at the congruence marks and the rotation about point X).

Step3: Use Given Length of AC

We know that \(AC = 14\) ft. Since \(RS\cong AC\) (because of the rigid transformation of rotation), then \(RS=AC = 14\) ft.

Answer:

14 ft (corresponding to the option "14 ft")