Question

Find the distance of the point $(2,3)$ form the line $2x-3y+9=0$ measurement along a line $x-y+1=0$.

Answer 1

$2x-3y+9=0$ ……..(i),

$x-y+1=0$ ………(ii)

Multiply equation (ii) by $2$ and subtract it from equation $\left(1\right)$

$2x-3y+9=0$

$2x-2y+2=0$

_____________

$-y+7=0$

_____________

$y=7,x=6$

Point of intersection $(6,7)$

Distance between $(2,3)$ and $(6,7)=\sqrt{(6-2{)}^2+(7-3{)}^2}$

$=4\sqrt{2}$ units

$\therefore$ Distance of the point $(2,3)$ from the line $2x-3y+9=0$ measured along line $x-y+1=0$ is $4\sqrt{2}$ units.