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

int main ()
{
   double x1, y1, x2, y2, x, y;
   double m, l;
   double a, b, c, D;
   double d;

   /* Seed the random number generator by the current time. This results
      in different random sequences in different runs. */
   srand((unsigned int)time(NULL));

   /* Generate the two points randomly in the unit square */
   x1 = (double)rand() / (double)RAND_MAX;
   y1 = (double)rand() / (double)RAND_MAX;
   x2 = (double)rand() / (double)RAND_MAX;
   y2 = (double)rand() / (double)RAND_MAX;
   printf("P = (%lf,%lf), Q = (%lf,%lf)\n", x1, y1, x2, y2);

   /* This assignment does not handle horizontal lines */
   if (y1 == y2) exit(1);

   /* Compute the perpendicular bisector */
   m = (x1 - x2) / (y2 - y1);
   l = (y1+y2)/2 - m*(x1+x2)/2;
   printf("The perpendicular bisector of PQ has equation:\n");
   printf("\ty = (%lf)x + (%lf).\n", m, l);

   d = (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2);
   printf("Distance between P and Q is %lf\n", sqrt(d));

   /* Find the two desired points on the perpendicular bisector by
      solving the quadratic equation ax^2 + bx + c = 0 */
   a = 1 + m*m; b = 2*(m*(l-y1)-x1); c = x1*x1 + (l-y1)*(l-y1) - d;
   D = b*b - 4*a*c; /* Discriminant */
   if (D < 0) exit(2); /* This should never happen */
   D = sqrt(D);
   x = (-b + D) / (2*a); y = m*x + l;
   printf("The first point is U = (%lf,%lf)\n", x, y);
   d = (x1-x)*(x1-x) + (y1-y)*(y1-y);
   printf("Distance between P and U is %lf\n", sqrt(d));
   d = (x2-x)*(x2-x) + (y2-y)*(y2-y);
   printf("Distance between Q and U is %lf\n", sqrt(d));
   x = (-b - D) / (2*a); y = m*x + l;
   printf("The second point is V = (%lf,%lf)\n", x, y);
   d = (x1-x)*(x1-x) + (y1-y)*(y1-y);
   printf("Distance between P and V is %lf\n", sqrt(d));
   d = (x2-x)*(x2-x) + (y2-y)*(y2-y);
   printf("Distance between Q and V is %lf\n", sqrt(d));

   exit(0);
}