Question

The image of a point is given by the rule ry = –x(x, y) → (–4, 9). What are the coordinates of its pre-image?

(–9, 4)
(–4, –9)
(4, 9)
(9, –4)

Answer 1

Reflection across the line y = −x sends (x,y) to (−y, −x).
Set (−y, −x) = (−4, 9). Then y = 4 and x = −9, so the pre-image is (−9, 4).