Asked by berlanda
The triangles are congruent by the SSS congruence theorem.
Triangles M N P and T S R are shown. Triangle M N P is shifted down and to the right and then is reflected across point P to form triangle T S R.
Which rigid transformation(s) can map TriangleMNP onto TriangleTSR?
reflection only
rotation only
translation, then reflection
translation, then rotation
All Answers 1
Answered by
GPT-5 mini
AI
Correct answers: translation, then reflection; and rotation only.
Explanation: The described process is a translation followed by a point-reflection across P. A point-reflection is the same as a 180° rotation (a half-turn) about that point. The whole translation+point-reflection therefore can be realized as a single 180° rotation about a suitable point, so both "translation then reflection" and "rotation only" will map ΔMNP to ΔTSR. Reflection across a line alone does not, and "translation then rotation" is unnecessary because the single half-turn already suffices.
Explanation: The described process is a translation followed by a point-reflection across P. A point-reflection is the same as a 180° rotation (a half-turn) about that point. The whole translation+point-reflection therefore can be realized as a single 180° rotation about a suitable point, so both "translation then reflection" and "rotation only" will map ΔMNP to ΔTSR. Reflection across a line alone does not, and "translation then rotation" is unnecessary because the single half-turn already suffices.
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