Question

In the xy - plane, line l has equation y= -x. Point P lies on l and has coordinates (-2,2). If l is rotated counterclockwise 45 degrees about the origin, what will be the coordinates of the image of P under this rotation.

Answer 1

Recall your rotation matrix.
(x,y) -> (x',y') where

x' = xcosθ - ysinθ
y' = xsinθ + ycosθ

So, plug in your θ.

You can easily check your work by noting that the point will rotate down to the x-axis.