# What is the orthocenter of a triangle with corners at #(1, 3)#, #(6, 2)#, and #(5, 4)#?

##### 1 Answer

#### Explanation:

Let: A(1, 3), B(6, 2) and C(5, 4) be the vertices of triangle ABC:

Slope of a line through points:

Slope of AB:

Slope of perpendicular line is 5.

Equation of the altitude from C to AB:

Slope of BC:

Slope of perpendicular line is 1/2.

Equation of the altitude from A to BC:

The intersection of the altitudes equating y's:

Thus the Orthocenter is at

To check the answer you can find the equation of altitude from B to AC and find the intersection of that with one of the other altitudes.