public class PointDemo {
	public static void main(String[] args) {
		//3-4-5 right triangle:

		Point A = new Point(3.0, 0.0);
		System.out.println("A == " + A);

		Point B = new Point(0.0, 4.0);
		System.out.println("B == " + B);

		System.out.println("Distance from A to B == " + A.distance(B));
		System.out.println("Distance from A to B == " + Point.distance(A, B));

		System.out.println("Midpoint of A and B == " + A.midpoint(B));

		Point origin = new Point(0.0, 0.0);
		System.out.println("Area == " + origin.area(A, B));
		System.out.println("Area == " + Point.area(origin, A, B));

		Point C = new Point(1.0, 1.0);
		System.out.println("theta(C) == " + C.theta());
		System.out.println(Point.contains(origin, A, B, C));

		System.exit(0);
	}
}

class Point {
	private double x;
	private double y;

	public Point(double x, double y) {
		this.x = x;
		this.y = y;
	}

	//Distance between this point and another one.

	public double distance(Point another) {
		final double dx = x - another.x;	//horizontal distance
		final double dy = y - another.y;	//vertical distance
		return Math.hypot(dx, dy);
	}

	public static double distance(Point p1, Point p2) {
		final double dx = p1.x - p2.x;	//horizontal distance
		final double dy = p1.y - p2.y;	//vertical distance
		return Math.hypot(dx, dy);
	}

	public Point midpoint(Point another) {	//method returns an object
		final double mx = (x + another.x) / 2.0;
		final double my = (y + another.y) / 2.0;
		return new Point(mx, my);
	}

	public double theta() {
		return Math.toDegrees(Math.atan2(y, x));
	}

	//Area of triangle whose vertices are this point, B, and C.
	//Instead of x and y, could say this.x and this.y.

	public double area(Point B, Point C) {
		return Math.abs(x * B.y + B.x * C.y + C.x * y
		              - y * B.x - B.y * C.x - C.y * x) / 2;
	}

	//Area of triangle whose vertices are points A, B, and C.

	public static double area(Point A, Point B, Point C) {
		return Math.abs(A.x * B.y + B.x * C.y + C.x * A.y
		              - A.y * B.x - B.y * C.x - C.y * A.x) / 2;
	}

	//Return true if triangle ABC contains point D.

	public static boolean contains(Point A, Point B, Point C, Point D) {
		return area(A, B, C)
			== area(D, A, B) + area(D, B, C) + area(D, C, A);
	}

	public String toString() {
		return "(" + x + ", " + y + ")";
	}
}