The three perpendicular bisectors of a triangle always intersect in one point. We can use coordinate geometry to show that the altitudes of a triangle intersect in one point, too. The three altitudes of triangle are shown here. They appear to intersect at the point . By finding their equations, we can prove this is true.

The slopes of sides  and are 0, , and 2. The altitude from is the vertical line . The slope of the altitude from is . Since the altitude goes through  its equation is . The slope of the altitude from is . Following this slope over to the -axis we can see that the -intercept is 8. So the equation for this altitude is .

We can now verify that lies on all three altitudes by showing that the point satisfies the three equations. By substitution, we see that each equation is true when and .