// Line.C
// (c) Burt Rosenberg 1996
// A program to generate the line equation from two
// points on the line.

#include<iostream.h>

void main() 
{
   float x1, y1 ;
   float x2, y2 ;
   float dx, dy ;
   float A, B, C ;

   // get two points
   cout << "Coordinates of first point on the line." << endl ;
   cout << " x: " ;
   cin >> x1 ;
   cout << " y: " ;
   cin >> y1 ;
   cout << "Coordinates of second point on the line." << endl ;
   cout << " x: " ;
   cin >> x2 ;
   cout << " y: " ;
   cin >> y2 ;

   // A xi + B yi + C = 0 , for i =1 , 2
   // subtract the equations gives
   // A ( x1 - x2 ) = B ( y2 - y1 ) 
   dx = x1 - x2 ;
   dy = y2 - y1 ;
   if ( dx == 0.0 ) 
   {
        // the line is vertical
        if ( dy == 0.0 ) 
        {
             cout << "The two points are identical," << endl ;
             cout << "No line can be derived." << endl ;
             return ;
        }
        // dx is 0, but dy is not. Hence B = 0. 
        A = 1.0 ;
        B = 0.0 ;
        C = - x1 ;
  }
  else if ( dy == 0.0 )
  {
        A = 0.0 ;
        B = 1.0 ;
        C = - y1 ;
   }
   else // the line is neither horizontal nor vertical.
   {
        A = 1.0 ;
        B = dx / dy ;
        C = - ( A*x1 + B*y1 ) ;
   }

   // output
   cout << A << " x + " << B << " y + " << C << " = 0 " << endl ;
}