Rectangle ABCD is shown. A is at negative 5, 1. B is at negative 5, 3. C is at negative 1, 3. D is at negative 1, 1.
Rectangle ABCD is rotated 180°. What rule shows the input and output of the rotation, and what is the new coordinate of A′?
(x, y) → (−x, −y); A′ is at (5, −1)
(x, y) → (−y, x); A′ is at (−1, −5)
(x, y) → (y, −x); A′ is at (1, 5)
(x, y) → (x, −y); A′ is at (−5, −1)
The correct rule for the rotation of 180° is:
(x, y) → (-x, -y)
Using this rule, the new coordinates for A will be (5, -1). Therefore, the correct answer is:
(x, y) → (-x, -y); A′ is at (5, -1)