How do I calculate the normal vector of a line segment?

Question

Suppose I have a line segment going from (x1,y1) to (x2,y2). How do I calculate the normal vector perpendicular to the line? I can find lots of stuff about doing this for planes in 3D, but no 2D stuff. Please go easy on the maths (links to worked examples, diagrams or algorithms are welcome), I'm a programmer more than I'm a mathematician ;)

Answer 1

The line "normal" or perpendicular to a line is the one having a slope that is the negative reciprocal of the slope of the line. So, first calculate the slope of the line between the two points, the flip it over and take the negative of it. Example: Point (1, 2) and (5, 8) The slope of the line between them is calculated by m = (y₂ - y₁)/(x₂ - x₁) so in this case: m = (8 - 2)/(5 - 1) = 6/4 = 3/2. The perpendicular has a slope of -2/3.

But that is just the slope. I'm unsure about the meaning of a vector perpendicular to a segment.. I would probably pick the normal line to go through the midpoint of the segment. The length of that line, I'm unsure of, perhaps the same length as the original segment.

Answer 2

Determine the vector from one point to the other.

Then use the dot product.