Question

Find the equation of the perpendicular to the line segment joining $(4,3)$ and $(-1,1)$ if it cuts off an intercept $-3$ from y-axis

Answer 1

let the line be $y=mx+c$

intercept of $-3$ from $y$ axis

$\therefore c=-3$

and

line is $\perp$ to the line segment joining $(4,3)$ and $(-1,1)$

$\therefore \left(m\right)\left(\frac{3-1}{4-(-1)}\right)-1$

$\frac{2}{5}m=-1$

$m=\frac{-5}{2}$

$\therefore$ line is $y=\frac{-5x}{2}-3$