# Linear transformation across a line

1. Nov 25, 2012

### 1up20x6

Using linear transformation reflection to find rotation

1. The problem statement, all variables and given/known data
Let $T1$ be the reflection about the line $−4x−1y=0$ and $T2$ be the reflection about the line $4x−5y=0$ in the euclidean plane.

The standard matrix of $T1 \circ T2$ is what?

Thus $T1 \circ T2$ is a counterclockwise rotation about the origin by an angle of how many radians?

2. Relevant equations

$\frac{1}{1+m^2}\begin{pmatrix} 1-m^2 & 2m\\ 2m & m^2-1 \end{pmatrix}$

3. The attempt at a solution

I've used the relevant equation above and found that $T1 \circ T2 = \begin{pmatrix} \frac{-455}{697} & \frac{-528}{697}\\ \frac{-455}{697} & \frac{-455}{697}\end{pmatrix}$ and had this verified, but I have no idea how to relate this into an amount of radians rotated.

Last edited: Nov 25, 2012
2. Nov 25, 2012

### tiny-tim

hi 1up20x6!

should be $\begin{pmatrix} \cos & \sin\\ -\sin & \cos\end{pmatrix}$