Notes: 8-6
Concurrence of the Altitudes of a Triangle
Concurrent:Three or more lines are concurrent if they intersect
in one point.
Theorem 8.4 - The altitudes of a triangle are concurrent.
Orthocenter: a point at which the altitudes of a triangle intersect
Finding the Orthocenter
1. Find the slope of each side of triangle.
2. Find the negative reciprocal.
3. Write the equation of the altitude from each vertex.
4. Set two equations equal to each other and solve for x.
Sub in for x and solve for y.
Ex. 1: The coordinates of the vertices of ΔPQR are P(0,0), Q(-2,6) and
R(4,0). Find the coordinates of the orthocenter.
Q
P
R
1
Ex. 2 The coordinates of the vertices of ΔABC are A(0,0), B(3,4), and C(2,1).
Find the coordinates of the orthocenter of the triangle.
Ex. 3 Find the coordinates of the orthocenter of ΔPQR if the vertices are
P(-3,4), Q(1,8), and R(3,4).
2