Question

Find the distance of the point $(-1,1)$ from the line $12(x+6)=5(y-2)$

Answer 1

The given equation of the line is $12(x+6)=5(y-2)$
$\Rightarrow 12x+72=5y-10$
$\Rightarrow 12x-5y+82=0$
Therefore, the distance of point $(-1,1)$ from the given line
$=\frac{\left|12\right(-1)+(-5\left)\right(1)+82|}{\sqrt{(12{)}^2+(-5{)}^2}}$ units $=\frac{|-12-5+82|}{\sqrt{169}}$ units $=\frac{\left|65\right|}{13}$ units $=5$ units