# 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 $L$:

$${R}_{\pi /2}=\left(\begin{array}{cc}\hfill 0\hfill & \hfill -1\hfill \\ \hfill 1\hfill & \hfill 0\hfill \end{array}\right)$$ |

Every point on $L$ can be represented as a multiple of the point $\overrightarrow{p}=\left(\begin{array}{c}\hfill 1\hfill \\ \hfill m\hfill \end{array}\right)$.

Notice ${\overrightarrow{p}}^{\prime}={R}_{\frac{\pi}{2}}\overrightarrow{p}=\left(\begin{array}{c}\hfill -m\hfill \\ \hfill 1\hfill \end{array}\right)$. Since every point on ${L}^{\prime}$ can be represented as a multiple of the point ${\overrightarrow{p}}^{\prime}$, the slope of ${L}^{\prime}$ is $\frac{-1}{m}$.

Title | example of rotation matrix |
---|---|

Canonical name | ExampleOfRotationMatrix |

Date of creation | 2013-03-22 15:09:16 |

Last modified on | 2013-03-22 15:09:16 |

Owner | swiftset (1337) |

Last modified by | swiftset (1337) |

Numerical id | 5 |

Author | swiftset (1337) |

Entry type | Example |

Classification | msc 15-00 |

Related topic | Slope |

Related topic | RotationMatrix |