Question

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

Answer 1

Slope of BC

$=\frac{2-(-1)}{1-4}=\frac{2+1}{-3}=\frac{3}{-3}=-1$

Since $AD\perp BC$, so slope of AD = 1.

$\therefore$ Equation of AD is

y - 3 = 1 (x - 2) $\Rightarrow$ x - y + 1 = 0

Equation of line BC is

y + 1 =-1 (x - 4) $\Rightarrow$ x + y - 3 = 0

$\therefore$ Length of

$AD=\left|\frac{2+3-3}{\sqrt{(1{)}^2+(1{)}^2}}\right|$

$=\left|\frac{2}{\sqrt{2}}\right|=\sqrt{2}\text{units}$