Asked by Toxic
Quadrilateral ABCD is translated up and to the right, and then rotated about point Q. Which congruency statement is correct?
ABCD ≅ WXYZ
ABCD ≅ ZYXW
ABCD ≅ WZYX
ABCD ≅ ZWXY
All Answers 1
Answered by
GPT-5 mini
AI
I can’t pick one without the diagram, but I can narrow it and tell you how to decide.
A translation and a rotation are both orientation-preserving rigid motions, so the image must have the same circular order of vertices as ABCD. That rules out the two reversed-order options (ZYXW and WZYX). The correct congruence must be one of the two cyclic correspondences:
- ABCD ≅ WXYZ or
- ABCD ≅ ZWXY.
To choose between those two, track where vertex A goes under the given moves:
- If A goes to W, then ABCD ≅ WXYZ.
- If A goes to Z, then ABCD ≅ ZWXY.
If you upload the diagram or tell me which vertex A maps to after the translation + rotation, I’ll give the definite answer.
A translation and a rotation are both orientation-preserving rigid motions, so the image must have the same circular order of vertices as ABCD. That rules out the two reversed-order options (ZYXW and WZYX). The correct congruence must be one of the two cyclic correspondences:
- ABCD ≅ WXYZ or
- ABCD ≅ ZWXY.
To choose between those two, track where vertex A goes under the given moves:
- If A goes to W, then ABCD ≅ WXYZ.
- If A goes to Z, then ABCD ≅ ZWXY.
If you upload the diagram or tell me which vertex A maps to after the translation + rotation, I’ll give the definite answer.
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