Question

On a coordinate plane, 2 triangles are shown. Triangle A B C has points (negative 3, negative 1), (negative 1, 2), and (negative 5, 3). Triangle R S T has points (1, 1), (3, 4), and (5, 0).
Triangle RST is rotated 180° about the origin, and then translated up 3 units. Which congruency statement describes the figures?

ΔRST ≅ ΔACB
ΔRST ≅ ΔABC
ΔRST ≅ ΔBCA
ΔRST ≅ ΔBAC

Answer 1

Rotate 180°: R(1,1)→R'(-1,-1), S(3,4)→S'(-3,-4), T(5,0)→T'(-5,0).
Translate up 3: R''(-1,2), S''(-3,-1), T''(-5,3).

Triangle ABC has A(-3,-1), B(-1,2), C(-5,3). So R'' = B, S'' = A, T'' = C, giving the correspondence R→B, S→A, T→C.

Thus ΔRST ≅ ΔBAC.