Question

Figure ABCDEF was reflected across the line y = –x to create figure A'B'C'D'E'F'.

On a coordinate plane, a 6-sided figure has points A prime (negative 2, negative 2), B prime (negative 4, 2), C prime (negative 2, 6), D prime (4, 6), E prime (6, 2), and F prime (4, negative 2).
What are the coordinates of the pre-image of F'?

(–2, 4)
(4, 2)
(2, –4)

Answer 1

Reflection across the line y = −x sends (x,y) → (−y, −x). To recover the pre-image, apply the same map to F'(4, −2):

(−(−2), −4) = (2, −4).

Answer: (2, −4).