How can I find a normal vector of a 2D line?

Question

I have a line with point a, (6, 12) and point b (45, 18).

To describe this line using vectors, the equation is L = [6, 12] +t [39, 6]

How would I go about finding the normal to this line?

see also [Given 2 points how do I draw a line at a right angle to the line formed by the two points?](http://stackoverflow.com/q/7469959/309483) for an elaborate explanation — Janus Troelsen, May 07 '13 at 11:34
possible duplicate of [How do I calculate the normal vector of a line segment?](http://stackoverflow.com/questions/1243614/how-do-i-calculate-the-normal-vector-of-a-line-segment) — duffymo, May 07 '13 at 13:01
I'm voting to close this question as off-topic because it is about mathematics, not programming. — Pang, Oct 07 '15 at 01:32

score 25 · Answer 1 · edited May 23 '17 at 12:13

25

if we define dx=x2-x1 and dy=y2-y1, then the normals are (-dy, dx) and (dy, -dx).

edited May 23 '17 at 12:13

Community

answered May 07 '13 at 11:32

Janus Troelsen

1

so in this case the normal is l= [-6, 39] and [6, -39] – Ian McLeod May 07 '13 at 11:37
1

your y2 is 18, your y1 is 12. so y2-y1 is 6. your x2 is 45 and your x1 is 6, so your x2-x1 is 39. so yes, (-dy,dx) is (-6,39) and (dy, -dx) is (6, -39). – Janus Troelsen May 07 '13 at 11:41

1 Answers1