(x, y) ⇒ (-y, x)
A point at y=1 on the y-axis will rotate to the point x = -1 on the x-axis when it is rotated 90° CCW about the origin. Hence the value of x for the image point is the opposite of the y-value of the original point.
A point at x=1 on the x-axis will rotate to the point y=1 on the y-axis when it is rotated 90° CCW about the origin. Hence the value of y for the image point is the x-value of the original point.
In summary, ...
... (x, y) ⇒ (-y, x)
_____
Comment on rotation matrices
The rotation matrix for rotatation through the angle θ CCW about the origin is ...
[tex]\left[\begin{array}{cc}\cos{(\theta)}&-\sin{(\theta)}\\\sin{(\theta)}&\cos{(\theta)}\end{array}\right][/tex]
When θ = 90°, this matrix becomes ...
[tex]\left[\begin{array}{cc}0&-1\\1&0\end{array}\right][/tex]
and multiplication by coordinates (x, y) gives ...
[tex]\left[\begin{array}{cc}0&-1\\1&0\end{array}\right]\times\left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}-y\\x\end{array}\right][/tex]
