Question

Triangle XYZ is rotated to create the image triangle X'Y'Z'.

On a coordinate plane, 2 triangles are shown. The first triangle has points X (negative 2, 2), Y (1, 2), Z (0, 4). The second triangle has points X prime (2, negative 2), Y prime (negative 1, negative 1), Z prime (0, negative 4).
Which rules could describe the rotation? Select two options.

R0, 90°
R0, 180°
R0, 270°
(x, y) → (–y, x)
(x, y) → (–x, –y)

Answer 1

Answers: R0, 180° and (x, y) → (–x, –y).

Reason: A 180° rotation about the origin sends (x,y) to (–x,–y). For example X(–2,2) → (2,–2) and Z(0,4) → (0,–4), which matches the image. (The given Y′ = (–1,–1) appears to be a typo; it should be (–1,–2) to match the 180° rotation.)