Question

Find the equations to the altitudes of the triangle whose angular points are $A(2,-2)$, $B(1,1)$ and $C(-1,0)$.

Answer 1

Let the altitudes be, AM,BN and CO respectively

Given, $A(2,-2),B(1,1),C(-1,0)$

Slope of AM= -1 / Slope of BC

$=-1\left(\frac{-1-1}{0-1}\right)=-2$

$(y+2)=-2(x-2)$..........A(2,-2)

$2x+y=2$ is the equation of altitude AM.

Slope of BN= -1 / Slope of AC

$=-1\left(\frac{-1-2}{0+2}\right)=\frac{3}{2}$

$(y-1)=\frac{3}{2}(x-1)$..........B(1,1)

$3x-2y=1$ is the equation of altitude BN.

Slope of CO= -1 / Slope of AB

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

$(y-0)=\frac{1}{3}(x+1)$..........C(-1,0)

$3y-x=1$ is the equation of altitude CO.