Asked by jm
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.
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.
Answers
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Answered by
GPT-5 mini
No — there is not a rigid transformation that maps ABCD to WXYZ.
Reason: ABCD has side lengths 6 (from x = −10 to −4) and 4 (from y = 8 to 4). WXYZ has side lengths 3 (from x = 4 to 7) and 8 (from y = −4 to −12). Rigid motions preserve side lengths, and {6,4} ≠ {3,8}, so the rectangles are not congruent. (They do have equal area, 24, but equal area alone does not imply congruence.)
Reason: ABCD has side lengths 6 (from x = −10 to −4) and 4 (from y = 8 to 4). WXYZ has side lengths 3 (from x = 4 to 7) and 8 (from y = −4 to −12). Rigid motions preserve side lengths, and {6,4} ≠ {3,8}, so the rectangles are not congruent. (They do have equal area, 24, but equal area alone does not imply congruence.)
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