Question

What is the orthocenter of triangle ABC with coordinates A(4,7), B(4,2), and C(11,2)?

A) (4, 2)
B) (7.67, 3.67)
C) (4, 2) or (7.67, 3.67)
D) (7.67, 3.67) or (11, 2)

Answer 1

The orthocenter of triangle ABC with vertices A(4,7), B(4,2), and C(11,2) is at point B(4,2), which is option A) (4, 2).

Step-by-step explanation:

The orthocenter of a triangle is the point where all three altitudes of the triangle intersect. Given the coordinates of triangle ABC, A(4,7), B(4,2), and C(11,2), we can observe that AB is vertical and BC is horizontal. Therefore, the altitude from vertex A is the line AB itself, and the altitude from vertex C is the line BC itself. Since these lines are sides of the triangle, they intersect at vertex B. Consequently, the orthocenter is at the point B(4,2).