Question

Find the equation of the line passing through the point $(5,2)$ and perpendicular to the line joining the points $(2,3)$ and $(3,-1)$.

Answer 1

The equation of line joining the points $(2,3)$ and $(3,-1)$ is

$\frac{y+1}{3+1}=\frac{x-3}{2-3}$

or, $y+1=-4x+12$

or, $y+4x=11$.....(1)

Now the equation of line perpendicular to the line (1) is $4x-y=c$......(2) { Where $c$ is constant].

Given the equation (2) passing through $(5,2)$ then we get, $c=18$.

So the equation of the line is $4x-y=18$.