# What is the orthocenter of a triangle with corners at #(3 ,1 )#, #(1 ,3 )#, and (5 ,2 )#?

##### 1 Answer

The orthocenter is at the point

#### Explanation:

Let's begin by writing the equation of the line that goes through point

The slope, m, of the line going through points

The slope, n, of any line perpendicular is

Use point slope form of the equation of a line to obtain the equation of a line that we desire:

Write the equation of a line that goes through point

The slope, m, of the line that goes through the points

The slope, n, of any line perpendicular is:

Again, Use the point slope form for the point

The orthocenter is at the intersection of these two lines:

The orthocenter is at the point