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.