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 perpendicular 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.

$\blacksquare$

Sources

• 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {2-3}$ The Linear Diophantine Equation: Exercise $7$