Question

Find the perpendicular distance between a point $(5,6)$ and a line $4x+3y+5=0$.

Answer 1

We have,

Line:$4x+3y+5=0$ and Point:$(5,6)$

We know that the perpendicular distance

$d=\left|\frac{ax+by+c}{\sqrt{a^2+b^2}}\right|$

Therefore,

$d=\left|\frac{4\times 5+3\times 6+5}{\sqrt{4^2+3^2}}\right|$

$d=\left|\frac{20+18+5}{\sqrt{16+9}}\right|$

$d=\left|\frac{43}{\sqrt{25}}\right|$

$d=\left|\frac{43}{5}\right|units$

Hence, this is the answer.