Question

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.

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).

Answer 1

The first choice is correct.

A 270° rotation about the origin sends (x,y) to (y,-x). Reflecting across the x-axis then sends (y,-x) to (y,x). So the combined map is (x,y) → (y,x). Applying it:

- A(−1,1) → (1,−1) = L
- B(−4,1) → (1,−4) = M
- C(−1,5) → (5,−1) = N

So ΔABC is mapped exactly onto ΔLMN by that rigid motion, hence the triangles are congruent.