Question

Find the length of the perpendicular drawn from
the point $(-3,-4)$ upon the straight line $12(x+6)=5(y-2)$.

Answer 1

$12(x+6)=5(y-2)$.

$12x-5y+82=0$

We know that standard form of straight line $ax+by+c=0$, perpendicular distance is = $\left|\frac{ax+by+c}{\sqrt{a^2+b^2}}\right|$

Given point is $(-3,-4)$

Therefore perpendicular distance = $\left|\frac{12\times -3+-5\times -4+82}{\sqrt{{12}^2+(-5{)}^2}}\right|$

$=\frac{66}{13}=5\frac{1}{13}$