# example of rotation matrix

You can use rotation matrices to show that if the slope of one line is $m$, then the slope of the line perpendicular to it is $\frac{-1}{m}$:

Let $L$ be a line with a slope of $m$ passing through the origin. The rotation matrix $R_{\frac{\pi}{2}}$ rotates $L$ into a line $L^{\prime}$ perpendicular to $L$:

 $R_{\pi/2}=\begin{pmatrix}0&-1\\ 1&0\\ \end{pmatrix}$

Every point on $L$ can be represented as a multiple of the point $\vec{p}=\begin{pmatrix}1\\ m\end{pmatrix}$.

Notice $\vec{p}^{\prime}=R_{\frac{\pi}{2}}\vec{p}=\begin{pmatrix}-m\\ 1\end{pmatrix}$. Since every point on $L^{\prime}$ can be represented as a multiple of the point $\vec{p}^{\prime}$, the slope of $L^{\prime}$ is $\frac{-1}{m}$.

Title example of rotation matrix ExampleOfRotationMatrix 2013-03-22 15:09:16 2013-03-22 15:09:16 swiftset (1337) swiftset (1337) 5 swiftset (1337) Example msc 15-00 Slope RotationMatrix