This is a Java Program to check whether a point lies below, above 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 the source code of the Java Program to Apply Above-Below-on Test to Find the Position of a Point with respect to a Line. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

`//This is a java program to check whether a point lies on, above or below the gievn line`

import java.util.Random;

import java.util.Scanner;

public class Position_Point_WRT_Line

`{`

public static void main(String args[])

`{`

Random random = new Random();

int x1, x2, y1, y2;

x1 = random.nextInt(10);

x2 = random.nextInt(10);

y1 = random.nextInt(10);

y2 = random.nextInt(10);

System.out.println("The Equation of the line is : (" + (y2 - y1)

+ ")x+(" + (x1 - x2) + ")y+(" + (x2 * y1 - x1 * y2) + ") = 0");

System.out.println("Enter the point : <x>,<y>");

Scanner scan = new Scanner(System.in);

int x, y;

x = scan.nextInt();

y = scan.nextInt();

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

if (s < 0)

System.out

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

else if (s > 0)

System.out

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

`else`

System.out.println("The point lies on the line");

scan.close();

`}`

`}`

Output:

$ javac Position_Point_WRT_Line.java $ java Position_Point_WRT_Line The Equation of the line is : (-2)x+(-9)y+(81) = 0 Enter the point : <x>,<y> 2 3 The point lies above the line or right side of the line

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