# Homework Help: Rotation in R2, around a line?

1. Oct 8, 2009

### DDrew

1. The problem statement, all variables and given/known data
Find the points fixed by f, and show it is a line. We know that f is an isometry.

0 $$\leq$$ $$\theta$$ < 2$$\Pi$$
f: R$$^{2}$$ $$\rightarrow$$ R$$^{2}$$
f(x) = Ax

A = | cos $$\theta$$ sin $$\theta$$ |
......| sin $$\theta$$ -cos $$\theta$$|

2. Relevant equations
fix(f) = {x | f(x) = x}

3. The attempt at a solution
fix(f) = | (x1)(cos $$\theta$$) + (x2)(sin $$\theta$$) = x1 |
...........| (x1)(sin $$\theta$$) + (x2)(cos $$\theta$$) = x2 |

The thing that confuses me the most is rotating about a line in R$$^{2}$$. I was under the impression you could only rotate around a point? Is there something I'm missing? I'm not looking for the answer so much as I'm looking to be pointed in the right direction.

I apologize for my messy matrix formatting.