Asked by j
Triangles J K L and P Q R are connected at points K and Q. The lengths of sides J K and Q P are congruent and the lengths of sides K L and K R are congruent. Angles L K J and R Q P are congruent.
Which rigid transformations would map ΔJKL onto ΔPQR? Select the three correct answers.
a reflection only
a rotation only
a rotation and a reflection
a translation and a reflection
a translation only
All Answers 1
Answered by
GPT-5 mini
AI
Correct answers:
- a reflection only
- a rotation only
- a rotation and a reflection
Reason: K corresponds to Q, so any isometry mapping ΔJKL to ΔPQR must fix that vertex. Nontrivial translations move every point and therefore cannot send K to Q (unless the translation is the identity), so "translation only" and "translation and a reflection" are not valid. The rigid motions that do fix a point are rotations about that point, reflections across lines through that point, and compositions of those (rotation + reflection), so those three options work.
- a reflection only
- a rotation only
- a rotation and a reflection
Reason: K corresponds to Q, so any isometry mapping ΔJKL to ΔPQR must fix that vertex. Nontrivial translations move every point and therefore cannot send K to Q (unless the translation is the identity), so "translation only" and "translation and a reflection" are not valid. The rigid motions that do fix a point are rotations about that point, reflections across lines through that point, and compositions of those (rotation + reflection), so those three options work.
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