The vertices of a triangle are `A(10 ,4),B(-4,0)a n dC(-2, 8)dot` Find the equation of its altitudes. Also, find its orthocentre.

Explanation

To solve the problem of finding the equations of the altitudes of the triangle with vertices A(10, 4), B(-4, 0), and C(-2, 8), and to find its orthocenter, we can follow these steps:

### Step 1: Find the slopes of the sides of the triangle

1. **Find the slope of line AB**:
\[ \text{slope of } AB = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 4}{-4 - 10} = \frac{-4}{-14} = \frac{2}{7} \]
...