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

 * Distance-of-Straight-Line-from-Origin.png

Let $d$ be the perpendicular distance between $L$ and $\tuple {0, 0}$.

We have: