Question

Triangle PQR was dilated according to the rule DO,2(x,y)(2x,2y) to create similar triangle P'Q'Q.

On a coordinate plane, (0, 0) is the center of dilation. Triangle P Q R is dilated to create triangle P Q prime Q. Triangle P Q R has points (negative 2, 2), (negative 2, 4), and (negative 1, 2). Triangle P prime Q prime Q has points (negative 4, 4), (negative 4, 8), and (negative 2, 4).

Which statements are true? Select two options.

∠R corresponds to ∠P'QQ'.
∠PQR corresponds to ∠QPQ'.
Segment QQ' is parallel to segment PP'.
Side RQ corresponds to side QQ'.
△PQR ≅ △P'Q'Q

Answer 1

Answers:
- ∠R corresponds to ∠P'QQ'. — True.
- Side RQ corresponds to side QQ'. — True.

Reasoning (brief):
- Dilation by 2 about the origin sends P(-2,2)→P'(-4,4), Q(-2,4)→Q'(-4,8), R(-1,2)→R'(-2,4). Note R' and the original Q have the same coordinates (-2,4).
- So angle at R corresponds to the angle at R' — which is the same geometric angle written as ∠P'QQ' — so the first statement is true.
- RQ corresponds to R'Q' under the dilation, and since R' = Q, R'Q' is the same segment as QQ', so statement 4 is true.
- The other statements are false (angles/sides are mismatched or the triangles are not congruent because scale factor ≠ 1).