Perpendicular Distance from Straight Line in Plane to Origin/Examples/Example 1

Examples of Perpendicular Distance from Straight Line in Plane to Origin
Let $\LL$ be the straight line defined by the equation:


 * $a x - b y = 1$

The distance $d$ from $\LL$ to the origin $\tuple {0, 0}$ is given by:


 * $d = \dfrac 1 {\sqrt {a^2 + b^2} }$

Proof
From Perpendicular Distance from Straight Line in Plane to Origin, $d$ is given by:


 * $d = \dfrac 1 {\sqrt {a^2 + \paren {-b}^2} }$

from which the result follows.