Question

Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected over the x-axis. The reflected figure is labeled figure C. Which best explains why figure A is congruent to figure C?

On a coordinate plane, triangle A has points (1, negative 2), (3, negative 2), (3, negative 5). Triangle B has points (4, 0), (6, 0), (6, negative 3). Triangle C has points (4, 0), (6, 0), (6, 3).
A Is congruent to B and B Is congruent to C
A Is congruent to A, B Is congruent to B, C Is congruent to C
Each triangle is a right triangle.
Each triangle is an isosceles triangle.

Answer 1

"A is congruent to B and B is congruent to C."

Reason: A translation and a reflection are rigid motions that preserve distances and angles, so A ≅ B and B ≅ C; therefore A ≅ C. (You can check the coordinates: A + (3 right, 2 up) = B, and reflecting B over the x-axis gives C.)