Answer:
Hence the orthocenter is (-2,12)
Step-by-step explanation:
We need to find the Orthocenter of ΔABC with vertices A(0,10) , B(4,10) and C(-2,4).
" Orthocenter of a triangle is a point of intersection, where three altitudes of a triangle connect ".
Step 1 : Find the perpendicular slopes of any two sides of the triangle.
Step 2 : Then by using point slope form, calculate the equation for those two altitudes with their respective coordinates.
Step 1 : Given coordinates are: A(0,10) , B(4,10) and C(-2,4)
Slope of BC = 
Perpendicular Slope of BC = -1
( since for two perpendicular lines the slope is given as: 
where
are the slope of the two lines. )
Slope of AC = 
Perpendicular Slope of AC= 
Step 2 : Equation of AD, slope(m) = -1 and point A = (0,10)


Equation of BE, slope(m) =\dfrac{-1}{3} and point B = (4,10)



----------(2)
Solving equations (1) and (2), we get
(x, y) = (-2,12)
Hence, the orthocenter is (-2,12).