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Question 8 • CMS 2026-2027 NC Math 2 CREDIT RECOVERY

Which of these triangle pairs can be mapped to each other using both a translation and a reflection across the line containing line segment AB ?

Answer

Image with description A four-sided figure A Y C B is divided by segment A C into two triangles, A B C and A Y C. Segment A C has double tick marks, segments B C and C Y have matching single tick marks, and an angle at C is marked.

Image with description Two separate triangles are shown. In triangle A B C, A is above B on a vertical side, and C is to the right. In triangle X Y Z, X is above Y on a vertical side, and Z is to the right. Segments A C and X Z have matching double tick marks, segments B C and Y Z have matching single tick marks, and angles C and Z have matching arc marks.

Image with description Two triangles are shown. Points X, A, Y, and B lie on the same vertical line, in that order from top to bottom. Point Z is to the left of the line, and point C is to the right. Segments X Z and A C have matching double tick marks, segments Y Z and B C have matching single tick marks, and angles Z and C have matching arc marks.

Image with description Two separate triangles are shown. In triangle A B C, A is above B on a vertical side, and C is to the right. In triangle X Y Z, Y is to the left of X, and Z is below X. Segments A C and X Z have matching double tick marks, segments B C and Y Z have matching single tick marks, and angles C and Z have matching arc marks.

Explanation

Reflecting triangle ABC across the line containing AB puts vertex C on the opposite side of that vertical line, matching the side of the line where Z lies in choice C. A translation can then align A with X and B with Y. The matching side and angle marks show the corresponding triangles are congruent, so the reflected triangle can be shifted into place without rotating it.

AI-written and checked against the verified answer.

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