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

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akposevictor akposevictor · Answer 1 · 2022-07-13T18:50:08+02:00

The congruency statement that describes the figure is: D. ΔRST ≅ ΔBAC.

A congruency statement is a statement that states that two triangles are congruent to each other.

180 degrees rotation around the origin will give us the rule: (x, y) → (-x, -y)

Therefore, applying this rule to triangle RST that was rotated, we would have:

R'(-1, -1)

S'(-3, -4)

T'(-5, 0)

Translating R'S'T' 3 units up, using the rule, (x, y + 3) will give us:

B(-1, 2)

A(-3, -1)

C(-5, 3)

Therefore, we can conclude that, D. ΔRST ≅ ΔBAC.

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