Question

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

Answer 1

The equation of BC is

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

$y+1=-x+4$

$x+y-3=0$

$AL=\left|\frac{2+3-3}{\sqrt{1+1}}\right|=\sqrt{2}$

Clearly, slope of BC having equation $x+y-3=0$ is - 1

So, slope of AL is 1 As is passes through A(2, 3) so its equation is

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