Find All Possible Coordinates of Parallelogram in C++

Find the all of the possible coordinates from the given three coordinates to make e parallelogram of a non-zero area. Suppose A, B, C are three given points we can have only three possible situations.

• AB, AC are sides, and BC is diagonal
• AB, BC are sides, and AC is diagonal
• BC, AC are sides, and AB is diagonal

So we can say that only three coordinates are possible, from which we can generate a parallelogram, if three coordinates are given. Since the opposite sides are equal, then AD = BC, and AB = CD, we will calculate the coordinate of the missing points D like below −

(Dx-Ax,Dy-Ay) = (Cx-Bx,Cy-By)
Dx = Ax+Cx-Bx
Dy = Ay+Cy-By

Example

#include<iostream>
using namespace std;
void printPoints(int ax, int ay, int bx, int by, int cx, int cy){
   cout << ax + bx - cx << ", " << ay + by - cy <<endl;
   cout << ax + cx - bx << ", " << ay + cy - by <<endl;
   cout << cx + bx - ax << ", " << cy + by - ax <<endl;
}
int main() {
   int ax = 5, ay = 0; //coordinates of A
   int bx = 1, by = 1; //coordinates of B
   int cx = 2, cy = 5; //coordinates of C
   printPoints(ax, ay, bx, by, cx, cy);
}

Output

4, -4
6, 4
-2, 1