Question

On a coordinate plane, 2 triangles are shown. Triangle A B C has points (negative 1, 1), (negative 4, 1) and (negative 1, 5). Triangle L M N has points (1, negative 1), (1, negative 4), and (5, negative 1).
Which best explains whether or not ΔABC ≅ ΔLMN?

The figures are congruent because a 270° rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN.
The figures are congruent because a 180 rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN.
The figures are not congruent because point B corresponds with point N and point C corresponds with point M.
The figures are not congruent because there is no rigid transformation or combination of rigid transformations that will map ΔABC onto ΔLMN.

Answer 1

The first choice is correct.

Rotate ΔABC 270° about the origin: (x,y) → (y,−x)
- A(−1,1) → (1,1)
- B(−4,1) → (1,4)
- C(−1,5) → (5,1)

Then reflect over the x-axis: (x,y) → (x,−y)
- (1,1) → (1,−1) = L
- (1,4) → (1,−4) = M
- (5,1) → (5,−1) = N

Thus a rigid motion maps ΔABC onto ΔLMN, so the triangles are congruent.