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.

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<time.h>`

`#include<stdlib.h>`

`#include<iostream>`

`#include<math.h>`

using namespace std;

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;

cout << "The Equation of the 1st line is : (" << (y2 - y1) << ")x+(" << (x1

- x2) << ")y+(" << (x2 * y1 - x1 * y2) << ") = 0\n";

int x, y;

cout << "\nEnter the point:";

cin >> x;

cin >> y;

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

if (s < 0)

cout << "The point lies below the line or left side of the line";

else if (s > 0)

cout << "The point lies above the line or right side of the line";

`else`

cout << "The point lies on the line";

return 0;

`}`

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Output:

$ g++ PointWRTLine.cpp $ a.out The Equation of the 1st line is : (3)x+(0)y+(-3) = 0 Enter the point:1 4 The point lies on the line The Equation of the 1st line is : (5)x+(-1)y+(-25) = 0 Enter the point:1 1 The point lies below the line or left side of the line The Equation of the 1st line is : (-6)x+(8)y+(-24) = 0 Enter the point:19 21 The point lies above the line or right side of the line ------------------ (program exited with code: 0) Press return to continue

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