Question

Which shows the image of rectangle ABCD after the rotation (x, y) → (–y, x)?

On a coordinate plane, 2 rectangles are shown. The first rectangle has points A (negative 2, 0), B (negative 1, 0), C (negative 1, 4), D (negative 2, 4). The second rectangle has points A prime (0, negative 2), B prime (0, negative 1), C prime (negative 4, negative 1), D prime (negative 4, negative 2).

On a coordinate plane, 2 rectangles are shown. The first rectangle has points A (negative 2, 0), B (negative 1, 0), C (negative 1, 4), D (negative 2, 4). The second rectangle has points A prime (1, negative 1), B prime (0, negative 1), C prime (0, negative 5), D prime (1, negative 5).

On a coordinate plane, 2 rectangles are shown. The first rectangle has points A (negative 2, 0), B (negative 1, 0), C (negative 1, 4), D (negative 2, 4). The second rectangle has points A prime (0, negative 3), B prime (0, negative 1), C prime (negative 4, negative 2), D prime (negative 4, negative 3).

On a coordinate plane, 2 rectangles are shown. The first rectangle has points A (negative 2, 0), B (negative 1, 0), C (negative 1, 4), D (negative 2, 4). The second rectangle has points A prime (0, negative 2), B prime (0, negative 1), C prime (4, negative 1), D prime (4, negative 2).

Answer 1

The first option. Applying (x,y) → (−y,x):

A(−2,0) → (0,−2)
B(−1,0) → (0,−1)
C(−1,4) → (−4,−1)
D(−2,4) → (−4,−2)

So A',B',C',D' are (0,−2),(0,−1),(−4,−1),(−4,−2), which matches the first figure.