Answer:
(10, 4)
Explanation:
The orthocenter of a triangle is the point of intersection of the three altitudes of the triangle.
Call points: A(0, 0), B(10, 4), C(8, 9)
Altitude from side AB to vertex C
Slope of AB = (4 - 0)/(10 - 0) = 2/5
Opposite vertex to AB: C(8, 9)
y = mx + b
9 = (-5/2) × 8 + b
18 = -40 + 2b
2b = 58
b = 29
y = (-5/2)x + 29
Altitude from side BC to vertex A
Slope of BC = (9 - 4)/(8 - 10) = -5/2
Opposite vertex of BC: A(0, 0)
y = mx + b
0 = (2/5)(0) + b
b = 0
y = (2/5)x
y = (-5/2)x + 29
y = (2/5)x
(-5/2)x + 29 = (2/5)x
-25x + 290 = 4x
-29x = -290
x = 10
y = (2/5)x = (2/5)(10) = 4
orthocenter = (10, 4)