How do you do a 90 degree counter-clockwise rotation around a point? I know around the origin it's $(-y,x)$, but what would it be around a point?
$$(-y – a,x – b)$$
Where $(a,b)$ is the rotation point.
[Math] 90 degree counter-clockwise rotation around a point
linear algebra
Related Solutions
$\hskip 1.3in$ 
$$\large y=\underbrace{\underbrace{A(\underbrace{x-p}_{\text{translate}})}_{\text{rotate}}+p}_{\text{translate back}} $$
For a $\frac{\pi}{2}$ anticlockwise rotation of $(x,y)$ about the origin, you can just take $(-y,x)$. This is about as short as you can get.
To see why, note that $\cos(\theta+\frac{\pi}{2}) = -\sin \theta$, and $\sin(\theta+\frac{\pi}{2}) = \cos \theta$. Hence the point $(r \cos \theta, r \sin \theta)$ will become $(r \cos (\theta+\frac{\pi}{2}), r \sin (\theta+\frac{\pi}{2}))$ = $(-r \sin \theta, r \cos \theta)$. Comparing coordinates gives the formula above.
Best Answer
Subtract the point, rotate around origin, add the point back:
$$(-(y-b)+a, (x-a) + b)$$