Read the result
The numerator tells you how far the point misses the line equation. The denominator rescales that miss into an actual perpendicular distance.
Coordinate geometry
Point-to-Line Distance
Find the perpendicular gap from a point to a line in general form, with the scaling of the normal made explicit.
Formula
d = |a x1 + b y1 + c| / sqrt(a^2 + b^2)
Result
Worked substitution
The denominator is the length of the line normal vector, so the formula scales correctly.
Where it helps
This is the clean route for clearance, offset, tolerance, and shortest-distance questions where the line is already in ax + by + c = 0 form.
Common slip
The formula expects general form. If your line is y = mx + c, rearrange it first to mx - y + c = 0.
Try it
Double a, b, and c together. The line is the same, so the distance should not change.