In a triangle ABC with vertices A(2,3) , B(4,-1),C(1,2).find the equation and the length of a altitude from the vertex A?

Question

In a triangle ABC with vertices A(2,3) , B(4,-1),C(1,2) find the
equation and the length of a altitude from the vertex A?

Aakash Sharma · Accepted Answer

Let AB be the altitude from vertex A and m be the slope of AD

Then AD ⊥ BC ⇒ slope of AD × slope of BC = – 1

$\Rightarrow m \times \frac{2 - (- 1)}{1 - 4} = - 1 \Rightarrow m \times \frac{3}{- 3} = - 1 \Rightarrow - m = - 1 \Rightarrow m = 1$

Since AD passes through A(2, 3) and has slope 1. So its equation is

y – 3 = 1 (x – 2)

⇒ x – y + 1 = 0