The perpendicular distance from point P(x1, y1) to line ax + by + c = 0 is d = |ax1 + by1 + c| / sqrt($a^2$ + $b^2$). This is one of the most frequently tested formulas. Common application: finding the radius of a circle tangent to a line, or checking if a point lies on a particular side of a line (by checking the sign of ax1 + by1 + c without absolute value).