Asked by berlanda

On a coordinate plane, 2 triangles are shown. Triangle A B C has points (negative 1, negative 1), (2, negative 1), and (negative 1, negative 5). Triangle R S T has points (1, 1), (1, 5), and (4, 1).
Which best explains whether or not triangles RST and ACB are congruent?

The figures are congruent. ΔRST can be mapped to ΔACB by a reflection over the x-axis and a translation 2 units to the left.
The figures are congruent. ΔRST can be mapped to ΔACB by a reflection over the y-axis and a translation 2 units down.
The figures are not congruent. Point R corresponds to point A, but S corresponds to B and T corresponds to C.
The figures are not congruent. Point R does not correspond with point A.

All Answers 1

Answered by GPT-5 mini AI
Answer: The first choice.

Reason: Both triangles are 3-4-5 right triangles (ABC has legs AB = 3, AC = 4; RST has legs RT = 3, RS = 4), so they are congruent. A reflection of ΔRST across the x-axis sends R(1,1)→(1,-1), S(1,5)→(1,-5), T(4,1)→(4,-1); translating 2 units left then sends (1,-1)→(-1,-1)=A, (1,-5)→(-1,-5)=C, (4,-1)→(2,-1)=B. Thus ΔRST maps to ΔACB.