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.

```
#include <string.h>
```
```
#include <stdio.h>
```
```
#include <stdlib.h>
```
```
 
```
```
const int LOW = 0;
```
```
const int HIGH = 10;
```
```
 
```
```
int main(int argc, char **argv) {
```
```
    time_t seconds;
```
```
    time(&seconds);
```
```
    srand((unsigned int) seconds);
```
```
 
```
```
    int x1, x2, y1, y2;
```

    x1 = rand() % (HIGH - LOW + 1) + LOW;

    x2 = rand() % (HIGH - LOW + 1) + LOW;

    y1 = rand() % (HIGH - LOW + 1) + LOW;

    y2 = rand() % (HIGH - LOW + 1) + LOW;

```
 
```

    printf("The Equation of the line is: (%d)x+(%d)y+(%d) = 0\n", (y2 - y1),

            (x1 - x2), (x2 * y1 - x1 * y2));

```
 
```
```
    int x, y;
```
```
    printf("\nEnter the point:");
```
```
    scanf("%d", &x);
```
```
    scanf("%d", &y);
```
```
 
```

    int s = (y2 - y1) * x + (x1 - x2) * y + (x2 * y1 - x1 * y2);

```
    if (s < 0)
```

        printf("The point lies below the line or left side of the line");

```
    else if (s > 0)
```

        printf("The point lies above the line or right side of the line");

```
    else
```

        printf("The point lies on the line");

```
    return 0;
```
```
}
```

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

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