Question

On a coordinate plane, 2 rectangles are shown. Rectangle P Q R S has points (1, 1), (1, 5), (3, 5), (1, 5). Rectangle P double-prime Q double-prime R double-prime S double-prime has points (negative 1, negative 1), (negative 5, negative 1), (negative 5, negative 3), (negative 1, negative 3).
Which rule describes a composition of transformations that maps pre-image PQRS to image P"Q"R"S"?

270 degree rotation about point 0 composition. Translation of negative 2 units x, 0 units y.
Translation of negative 2 units x, 0 units y composition 270 degree rotate about point 0.
270 degree rotation about point 0 composition reflected across the y-axis
Reflected across the y-axis composition 270 degree rotation about point 0.

Answer 1

Reflected across the y-axis composition 270 degree rotation about the origin.

Reason: 270° rotation about the origin sends (x,y) to (y, −x). Reflecting across the y‑axis after that sends (y, −x) to (−y, −x). For the vertices:
- (1,1) -> (1,−1) -> (−1,−1)
- (1,5) -> (5,−1) -> (−5,−1)
- (3,5) -> (5,−3) -> (−5,−3)
- (3,1) -> (1,−3) -> (−1,−3)

These are the image points, so the correct composition is: reflect across the y‑axis ∘ rotate 270° about the origin.