Question

Find the perpendicular distance from the origin of the perpendicular from the point $(1,2)$ upon the straight line
$x-\sqrt{3}y+4=0$

Answer 1

$x-\sqrt{3}y+4=0$

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

Given point is $(1,2)$

Therefore perpendicular distance, $d=\left|\frac{1\times 1-\sqrt{3}\times 2+4}{\sqrt{1^2+(\sqrt{3}{)}^2}}\right|$

$\Rightarrow d=\frac{5-2\sqrt{3}}{2}$