# Euler line (its slope related to the slopes of the sides of a triangle)

## Description

In geometry, the Euler line is a line determined from any triangle that is not equilateral. It passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the nine-point circle of the triangle. In any triangle, the orthocenter, circumcenter and centroid are collinear.

The slope of the Euler line (if finite) is expressible in terms of the slopes of the sides of the triangle.

## Variables

m_{E} | The slope of the Euler line in a Cartesian coordinate system (dimensionless) |

m_{1} | The slope of a side of the triangle in a Cartesian coordinate system (dimensionless) |

m_{2} | The slope of a side of the triangle in a Cartesian coordinate system (dimensionless) |

m_{3} | The slope of a side of the triangle in a Cartesian coordinate system (dimensionless) |