Question

Find the length of the perpendicular drawn from
the point $(4,5)$ upon the straight line $3x+4y=10$.

Answer 1

$3x+4y=10$

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 $(4,5)$

Therefore perpendicular distance = $\left|\frac{4\times 3+4\times 5-10}{\sqrt{3^2+4^2}}\right|$

$\Rightarrow \frac{22}{5}$