(Geometry: point position) Programming Exercise 3.32 shows how to test whether a point is on the left side of a directed line, on the right, or on the same line. Write the methods with the following headers:

// (Geometry: point position) Programming Exercise 3.32 shows how to test whether
// a point is on the left side of a directed line, on the right, or on the same line. Write
// the methods with the following headers:
// */
// /** Return true if point (x2, y2) is on the left side of the
// * directed line from (x0, y0) to (x1, y1) */
// public static boolean leftOfTheLine(double x0, double y0,
// double x1, double y1, double x2, double y2)
// /** Return true if point (x2, y2) is on the same
// * line from (x0, y0) to (x1, y1) */
// public static boolean onTheSameLine(double x0, double y0,
// double x1, double y1, double x2, double y2)
// /** Return true if point (x2, y2) is on the
// * line segment from (x0, y0) to (x1, y1) */
// public static boolean onTheLineSegment(double x0, double y0,
// double x1, double y1, double x2, double y2)
// Write a program that prompts the user to enter the three points for p0, p1, and p2
// and displays whether p2 is on the left of the line from p0 to p1, right, the same
// line, or on the line segment.
import java.util.Scanner;

public class Exercise_06_39 {
	/** Main Method */
	public static void main(String[] args) {
		Scanner input = new Scanner(System.in); // Create a Scanner

		//	Prompt the user to enter the three points for p0, p1, and p2
		System.out.print("Enter three points for p0, p1, and p2: ");
		double x0 = input.nextDouble();
		double y0 = input.nextDouble();
		double x1 = input.nextDouble();
		double y1 = input.nextDouble();
		double x2 = input.nextDouble();
		double y2 = input.nextDouble();

		// Displays whether p2 is on the left of the line from  
		// p0 to p1, right, the same line, or on the line segment.
		System.out.print("(" + x2 + ", " + y2 + ") is on the ");
		if (onTheLineSegment(x0, y0, x1, y1, x2, y2))
			System.out.print("line segment ");
		else if (leftOfTheLine(x0, y0, x1, y1, x2, y2))
			System.out.print("left side of the line ");
		else if (onTheSameLine(x0, y0, x1, y1, x2, y2))
			System.out.print("same line ");
		else 
			System.out.print("right side of the line");
		System.out.println(
			"from " + "(" + x0 + ", " + y0 + ") to (" + x1 + ", " + y1 + ")");
	}

	/** Return true if point (x2, y2) is on the left side of the
	* directed line from (x0, y0) to (x1, y1) */
	public static boolean leftOfTheLine(double x0, double y0,
	double x1, double y1, double x2, double y2){
		return pointPosition(x0, y0, x1, y1, x2, y2) > 0;
	}

	/** Return true if point (x2, y2) is on the same
	* line from (x0, y0) to (x1, y1) */
	public static boolean onTheSameLine(double x0, double y0,
	double x1, double y1, double x2, double y2){
		return pointPosition(x0, y0, x1, y1, x2, y2) == 0;
	}

	/** Return true if point (x2, y2) is on the
	* line segment from (x0, y0) to (x1, y1) */
	public static boolean onTheLineSegment(double x0, double y0,
	double x1, double y1, double x2, double y2) {
		return (pointPosition(x0, y0, x1, y1, x2, y2) == 0 &&
				 (x2 > x0) && (y2 > y0) && (x2 < x1) && (y2 < y1));
	}

	/** Method pointPosition returns the position of p2 to p0 and p1 */
	public static double pointPosition(double x0, double y0,
	double x1, double y1, double x2, double y2) {
		// Calculate point position
		return (x1 - x0) * (y2 - y0) - (x2 - x0) * (y1 - y0);
	}
}