Question

Triangle RST is rotated 180° about the origin, and then translated up 3 units. Which congruency statement describes the figures?

ΔRST ≅ ΔACBΔRST ≅ ΔABCΔRST ≅ ΔBCA ΔRST ≅ ΔBAC

Answer 1

So the new answer should be BAC▲RST

Hope that helps

Answer 2

Answer: ΔRST ≅ ΔBAC

Explanation:

We know that To rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y).

Thus, The coordinates of Δ RST becomes

R (1,1) → R'(-1,-1)

S (3,4) → S'(-3,-4)

T(-5,0) → T'(5,0)

Also ΔRST after rotation is translated up 3 units. , so we apply the rule (x,y)→(x,y+3)

R'(-1,-1)→R"(-1,-1+3)=R"(-1,2)→ B

S'(-3,-4) → S"(-3,-4+3) = R"(-3,-1) → A

C'(-5,0) → C"(-5,0+3) → C"(-5,3) → C

As rotation and translation both are rigid transformation that maps only congruent figures.

Therefore, ΔRST ≅ Δ BAC