Find the orthocenter of a triangle with the coordinates (1,0) (4,7) (8,-3)
+23245 The orthocenter of the triangle is the point of intersection of the three altitudes.
An altitude of a triangle is a line that passes through a vertex and is perpendicular to the opposite side.
Label these points: A = (1,0) B = (4,7) C = (8,-3)
Find the slope of AB: slope = (7 - 0) / (4 - 1) = 7/3
Find the slope of AC: slope = (-3 - 0) / (8 - 1) = -3/7
Since these slopes are negative reciprocals, AB is perpendicular to AC.
Therefore, angle(A) is a right angle.
In the special case of a right triangle, the three altitudes intersect at the vertex of the right triangle; in this case, the point (1,0).
