**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).**