Distance From Point To Line

From CGAFaq

The distance between a point C and a line L is the distance from C to the nearest point N on L. The nearest point is given by the fact that the line between N and C must be perpendicular to L. Thus:

Let the line L be parametrized by
$L(t) = P + tD$
where
$P$ is a point on the line
$D$ is a vector denoting the direction of the line

The condition for perpendicularity is
$dot(N - C, D) = 0$

Using the properties of the dot product yields
$dot(L(s) - C, D) = 0$
$dot(P + sD - C, D) = 0$
$dot(sD, D) + dot(P - C, D) = 0$
$s * dot(D, D) + dot(P - C, D) = 0$
$s = -dot(P - C, D) / dot(D, D)$
$s = dot(C - P, D) / dot(D, D)$