# Rotating a Rectangle Help

• August 13th 2008, 06:43 AM
nickd_101
Rotating a Rectangle Help
Hello,
I'm trying to work on rotating a rectangle for some computer code. I know the top left and right co-ordinates and the rectangle size, but I'm trying to figure out how I'd determine the relative co-ordinates of the bottom points that would be joined to create the rectangle. Is there a formula for this?

I haven't done maths in a while so please excuse me if this is straightforward!

Thanks
• August 13th 2008, 07:44 AM
Chop Suey
You can use a rotation matrix.

Suppose you have a point P(x,y). Let the image point be B(x,y) after a rotation of $\theta$ radians. The coordinates of the image point can be found by matrix multiplication:

$\left[ {\begin{array}{*{20}c}
{\cos{\theta}} & {-\sin{\theta}} \\
{\sin{\theta}} & {\cos{\theta}} \\
\end{array}}\right]
\left[ {\begin{array}{*{20}c}
{x} \\
{y} \\
\end{array}} \right] =
\left[ {\begin{array}{*{20}c}
{x'} \\
{y'} \\
\end{array}} \right]

$