Java Program to Check Whether a Given Point Lies Inside a Triangle or not

import java.awt.Point;
import static java.lang.Math.*;
public class Main
{
    public static void main(String[] args)
    {       
        //Coordinates of the triangle
        Point a = new Point(0,0);
        Point b = new Point(20,0);
        Point c = new Point(10,30);
        //Coordinates of the Point
        Point p = new Point(10,15);
        // Checks if the point lies in
        if(checkPointLoc(a,b,c,p))
            System.out.println("The point lies inside the triangle");
        else
            System.out.println("The point does not lie inside the triangle");
    }
    
    // Checks if the areas of the three small triangles add upto the primary triangle
    static boolean checkPointLoc(Point a, Point b, Point c, Point p)
    {
        double primaryTriangleAr = AreaOfTriangle(a,b,c);
        double area1 = AreaOfTriangle(a,b,p);
        double area2 = AreaOfTriangle(a,p,c);
        double area3 = AreaOfTriangle(p,b,c);
        if(primaryTriangleAr==area1+area2+area3)
            return true;
        return false;
    }
    // Calculates the area of the triangle
    static double AreaOfTriangle(Point A, Point B, Point C)
    {
        return Math.abs((A.x*(B.y-C.y) + B.x*(C.y-A.y)+ C.x*(A.y-B.y))/2.0);
    }
}

Output:

The point lies inside the triangle