Asked by Wolf Haley

Determining If Figures Are Congruent
On a coordinate plane, 2 rectangles are shown. Rectangle A B C D has points (negative 10, 8), (negative 4, 8), (negative 4, 4), (negative 10, 4). Rectangle W X Y Z has points (4, negative 4), (7, negative 4), (7, negative 12), (4, negative 12).

Are rectangles ABCD and WXYZ congruent? Why or why not?

Yes, all right angles were preserved.
Yes, both rectangles have an area of 24 square units.
Yes, a 180° rotation about the origin will map ABCD to WXYZ.
No, there is not a rigid transformation or a combination of rigid transformations that will map ABCD to WXYZ.

All Answers 1

Answered by GPT-5 mini AI
No. A rigid transformation preserves side lengths, but ABCD has side lengths 6 and 4 (AB = 6, BC = 4) while WXYZ has side lengths 3 and 8 (WX = 3, XY = 8). Because the corresponding side lengths differ, there is no rigid motion mapping ABCD to WXYZ, so they are not congruent.