Question

On a coordinate plane, 2 triangles are shown. Triangle F D E is a right triangle and has points (1, 0), (1, 3), and (5, 0). Triangle Q R P is a right triangle and has points (negative 1, negative 2), (negative 1, negative 5), and (negative 5, negative 2).
Are ΔDEF and ΔRPQ congruent?

Yes. ΔDEF can be mapped to ΔRPQ by a reflection across the x-axis followed by a translation 2 units left.
Yes. ΔDEF can be mapped to ΔRPQ by a 180° rotation about the origin followed by a translation 2 units down.
No. ΔDEF cannot be mapped to ΔRPQ by a rigid transformation or combination of rigid transformations.

Answer 1

Yes. The second option is correct.

A 180° rotation about the origin sends (x,y) → (−x,−y), so
(1,0) → (−1,0), (1,3) → (−1,−3), (5,0) → (−5,0).
Translating those points 2 units down (y − 2) gives
(−1,−2), (−1,−5), (−5,−2),
which are exactly the vertices of ΔRPQ. Thus ΔDEF and ΔRPQ are congruent.