Find the coordinates of the orthocenter of triangle ABC with vertices A (2, 6), B (8, 6), and C (6, 2).

A. (5, 4)

B. (1, 2)

C. (6,4)

D. (6, 8)

By elimination, we can remove B and D because they lie outside of the triangle.

We know that the orthocenter is where the altitudes of a triangle intersect.

The side AB is horizontal, so you know that the altitude of AB is vertical. The altitude of AB also connects to vertex C.

Since the orthocenter must lie on the altitude of AB, and the altitude is vertical, the orthocenter must lie directly above vertex C. This means that the x-coordinate of the orthocenter is the same as the x-coordinate of vertex C.

The only choices where the x-coordinate is the same as the one for vertex C is C and D. But we eliminated choice D, meaning the answer is choice C.