# C Program to Apply Above-Below-on Test to Find the Position of a Point with Respect to a Line

This is a C Program to check whether point lies above, below or on the line. For any point t (xt, yt) on the plane, its position with respect to the line L connecting p and q is found by calculating the scalar s:
s = A xt + B yt + C
If s < 0, t lies in the clockwise halfplane of L; if s > 0, t lies on the counter-clockwise halfplane; if s = 0, t lies on L.
For example, the equation of the line connecting points (2, 2) and (4, 5) is -3x + 2y + 2 = 0. The point (6, 3) lies in the clockwise halfplane of this line, because (-3)(6) + (2)(3) + 2 = -10. Conversely, the point (0, 5) lies in the other halfplane as (-3)(0) +(2)(5) +2 = 12.

Here is source code of the C Program to Apply Above-Below-on Test to Find the Position of a Point with respect to a Line. The C program is successfully compiled and run on a Linux system. The program output is also shown below.

1. `#include <string.h>`
2. `#include <stdio.h>`
3. `#include <stdlib.h>`
4. ` `
5. `const int LOW = 0;`
6. `const int HIGH = 10;`
7. ` `
8. `int main(int argc, char **argv) {`
9. `    time_t seconds;`
10. `    time(&seconds);`
11. `    srand((unsigned int) seconds);`
12. ` `
13. `    int x1, x2, y1, y2;`
14. `    x1 = rand() % (HIGH - LOW + 1) + LOW;`
15. `    x2 = rand() % (HIGH - LOW + 1) + LOW;`
16. `    y1 = rand() % (HIGH - LOW + 1) + LOW;`
17. `    y2 = rand() % (HIGH - LOW + 1) + LOW;`
18. ` `
19. `    printf("The Equation of the line is: (%d)x+(%d)y+(%d) = 0\n", (y2 - y1),`
20. `            (x1 - x2), (x2 * y1 - x1 * y2));`
21. ` `
22. `    int x, y;`
23. `    printf("\nEnter the point:");`
24. `    scanf("%d", &x);`
25. `    scanf("%d", &y);`
26. ` `
27. `    int s = (y2 - y1) * x + (x1 - x2) * y + (x2 * y1 - x1 * y2);`
28. `    if (s < 0)`
29. `        printf("The point lies below the line or left side of the line");`
30. `    else if (s > 0)`
31. `        printf("The point lies above the line or right side of the line");`
32. `    else`
33. `        printf("The point lies on the line");`
34. `    return 0;`
35. `}`

Output:

```\$ gcc PointWRTLine.c
\$ ./a.out

The Equation of the line is: (-1)x+(2)y+(-8) = 0

Enter the point:2 3
The point lies below the line or left side of the line```

Sanfoundry Global Education & Learning Series – 1000 C Programs. 