How do i rotate figures around a point

[MathPerson]

Lets say i have triangle abc and a is (1,1) b is (1,2) and c is (2,0) and i want to rotate it D Degrees around point (0,0). How do i do this?

 

[HallsofIvy]

Rotation around (0, 0) through angle D maps point (x, y) to \(\displaystyle \begin{bmatrix}cos(\theta) & -sin(\theta) \\ sin(\theta) & cos(\theta) \end{bmatrix}\begin{bmatrix}x \\ y \end{bmatrix}= \begin{bmatrix}x cos(\theta)- y sin(\theta) \\ x sin(\theta) + y cos(\theta) \end{bmatrix}\).

 

[Romsek]

Lets say i have triangle abc and a is (1,1) b is (1,2) and c is (2,0) and i want to rotate it D Degrees around point (0,0). How do i do this?

http://en.wikipedia.org/wiki/Rotation_matrix

find the matrix R for your angle. Use it to rotate each vertex point p=(x,y) to the new point p' = Rp. Connect your new vertices p'.