Perpendicular Distance from Straight Line in Plane to Origin

Theorem
Let $L$ be the straight line embedded in the cartesian plane whose equation is given as:
 * $a x + b y = c$

Then the perpendicular distance $d$ between $L$ and $\tuple {0, 0}$ is given by:


 * $d = \size {\dfrac c {\sqrt {a^2 + b^2} } }$

Proof
From Perpendicular Distance from Straight Line in Plane to Point, the perpendicular distance $d$ between $L$ and the point $\tuple {x_0, y_0}$ is gven by:
 * $d = \dfrac {\size {a x_0 + b y_0 + c} } {\sqrt {a^2 + b^2} }$

The result follows by setting $x_0 = 0$ and $y_0 = 0$.