Reflection through a line I need to find the matrix of reflection through line $y=- \frac 23 x$ . 
I'm trying to visualise a vector satisfying this. The standard algorithm states that we need to find the angle this line makes with $x$ axis and the transformation matrix can be seen as $R_\alpha T_0 R_{-\alpha}.$
I'm not sure how to proceed. I can't visualise the angle it makes with $x$ axis. 
Is there a procedure to think about such reflections? 
 A: Alternatively to the comment above (which requires a bit of trig), where does your matrix T send $\left( \begin{matrix}
   3  \\
   -2  \\
\end{matrix} \right)$ and $\left( \begin{matrix}
   2  \\
   3  \\
\end{matrix} \right)$ which are on and perpendicular to your line respectively. Now can you find a and b in terms of x and y so that $$\left( \begin{matrix}    x  \\    y  \\ \end{matrix} \right)=a\left( \begin{matrix}    3  \\    -2  \\ \end{matrix} \right)+b\left( \begin{matrix}    2  \\    3  \\ \end{matrix} \right)$$ Finally, apply T to find T$\left( \begin{matrix}
   x  \\
   y  \\
\end{matrix} \right)$
A: Notice that vectors on this line have  the form $(1, -\frac{2}{3} )$, and an orthogonal vector would be $(\frac{2}{3}, 1) $. A very straightforward procedure could be to reflect the vectors $(0,1)$ and $(1,0)$ orthogonally in this line. Have you done this before? Once you have determined the images of the basis vectors, you can figure out what the matrix columns should look like.
