Find 2 point with same distance from A

Question

I have a math problem. I have location (x,y) of point A, B, and a number (x). I want to calculate the location of point C, D. CD is perpendicular with AB and AC = AD = x.

This is the picture describe my problem:

my problem

Can anyone help me on this?

Thanks

I think this is not a right place to post this question..... — Venk, Apr 30 '13 at 08:44
You have a math problem, this is a site for helping people with programming problems. — High Performance Mark, Apr 30 '13 at 08:47
Hey your question is similar to http://stackoverflow.com/questions/133897/how-do-you-find-a-point-at-a-given-perpendicular-distance-from-a-line .Refer this question. — rahulserver, Apr 30 '13 at 08:54
@HighPerformanceMark then why are the tags geometry and distance on SO? — rahulserver, Apr 30 '13 at 08:59
I did not see the possible duplicate before posting my answer, but interestingly that question (and the answer) got a lot of upvotes and no closing votes ... — Martin R, Apr 30 '13 at 09:11
@HighPerformanceMark sorry because I develop for iphone so I post my question here. — haisergeant, Apr 30 '13 at 09:29

score 2 · Accepted Answer · answered Apr 30 '13 at 08:55

You did not specify a programming language, but from your previous questions it seems that you have some experience with (Objective-)C and Core Graphics on iOS, so this would be a solution using C and Core Graphics data structures:

// Your input data:
CGPoint A = ...
CGPoint B = ...
CGFloat x = ...

// Vector from A to B:
CGPoint vecAB = CGPointMake(B.x - A.x, B.y - A.y);
// Length of that vector:
CGFloat lenAB = hypotf(vecAB.x, vecAB.y);
// Perpendicular vector, normalized to length 1:
CGPoint perp = CGPointMake(-vecAB.y/lenAB, vecAB.x/lenAB);

CGPoint C = CGPointMake(A.x + x * perp.x, A.y + x * perp.y);
CGPoint D = CGPointMake(A.x - x * perp.x, A.y - x * perp.y);

score 1 · Answer 2 · edited May 23 '17 at 12:04

1

Your question is similar to How do you find a point at a given perpendicular distance from a line? . If you want further mathemetical details, you can refer: http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html

edited May 23 '17 at 12:04

Community

1
1

answered Apr 30 '13 at 08:57

rahulserver

10,411
24
90
164

Find 2 point with same distance from A

2 Answers2