How to find coordinates of a 2d equilateral triangle in C?

Question

I have the coordinates (x,y) of 2 points. I want to build the third point so that these 3 points make an equilateral triangle.

How can I calculate the third point?

Thank you

Answer 1

After reading the posts (specially vkit's) I produced this simple piece of code which will do the trick for one direction (remember that there are two points). The modification for the other case shold be trivial.

#include<stdio.h>
#include<math.h>

typedef struct{
  double x;
  double y;
} Point;

Point vertex(Point p1, Point p2){
  double s60 = sin(60 * M_PI / 180.0);    
  double c60 = cos(60 * M_PI / 180.0);

  Point v = {
    c60 * (p1.x - p2.x) - s60 * (p1.y - p2.y) + p2.x,
    s60 * (p1.x - p2.x) + c60 * (p1.y - p2.y) + p2.y
  };

  return v;
}