Question

Shape 1 and shape 2 are plotted on a coordinate plane. Which statement about the shapes is true?

A. Shape 1 and shape 2 are not congruent.
B. A translation will prove that shape 2 is congruent to shape 1.
C. A rotation and a translation will prove that shape 2 is congruent to shape 1.
D. A reflection, a rotation, and a translation will prove that shape 2 is congruent to shape 1.

Answer 1

D. A reflection, a rotation, and a translation will prove that shape 2 is congruent to shape 1.

Explanation:

The shapes are mirror images of each other, so a reflection of shape 2 would make it be able to be superimposed on shape 1 exactly. Then you need to rotate shape 2 to get it in the same orientation as shape 1. Finally, you apply a translation to shape 2, and it will be superimposed exactly over shape 1. That proves shape 1 and shape 2 are congruent.

Answer 2

D. A reflection, a rotation, and a translation will prove that shape 2 is congruent to shape 1.