# Equation of the Altitudes of a Triangle

To find the equation of the altitude of a triangle, we examine the following example: Consider the triangle having vertices , and .

First we find the slope of side :

The altitude is perpendicular to side .

The slope of

Since the altitude passes through the point , using the point-slope form of the equation of a line, the equation of is

This is the required equation of the altitude from to .

The slope of side is

The altitude is perpendicular to side .

The slope of

Since the altitude passes through the point , using the point-slope form of the equation of a line, the equation of is

This is the required equation of the altitude from to .

The slope of side is

The altitude is perpendicular to side .

The slope of

Since the altitude passes through the point , using the point-slope form of the equation of a line, the equation of is

This is the required equation of the altitude from to .