How to rotate a 2D point

Problem/Question/Abstract:

How to rotate a 2D point

Answer:

In 2-D, the 2 x 2 matrix is very simple. If you want to rotate a column vector v by t degrees using matrix M, use



M = {{cos t, -sin t}, {sin t, cos t}}



in M * v.

If you have a row vector, use the transpose of M (turn rows into columns and vice versa). If you want to combine rotations, in 2-D you can just add their angles, but in higher dimensions you must multiply their matrices.