# condition of orthogonality

Let two straight lines of the $xy$-plane have the slopes ${m}_{1}$ and ${m}_{2}$. The lines are at right angles^{} to each other iff ${m}_{1}$ and ${m}_{2}$ are the opposite inverses^{} of each other, i.e. iff (http://planetmath.org/Biconditional^{})

$${m}_{1}{m}_{2}=-1.$$ |

Example. The lines $y=(1+\sqrt{2})x$ and $y=(1-\sqrt{2})x$ are at right angles to each other.

Title | condition of orthogonality |

Canonical name | ConditionOfOrthogonality |

Date of creation | 2013-03-22 14:48:05 |

Last modified on | 2013-03-22 14:48:05 |

Owner | pahio (2872) |

Last modified by | pahio (2872) |

Numerical id | 14 |

Author | pahio (2872) |

Entry type | Result |

Classification | msc 15A57 |

Classification | msc 51F20 |

Synonym | condition of perpendicularity |

Related topic | OrthogonalCurves |

Related topic | InverseNumber |

Related topic | OppositeNumber |

Related topic | NormalLine |

Related topic | AngleBetweenTwoLines |

Related topic | PerpendicularityInEuclideanPlane |

Related topic | Evolute2 |

Related topic | ExampleOfFindingCatacaustic |

Defines | opposite inverse |