(Geometry: point position) Given a directed line from point p0(x0, y0) to p1(x1, y1), you can use the following condition to decide whether a point p2(x2, y2) is on the left of the line, on the right, or on the same line (see Figure 3.11):

/*
(Geometry: point position) Given a directed line from point p0(x0, y0) to p1(x1,
y1), you can use the following condition to decide whether a point p2(x2, y2) is
on the left of the line, on the right, or on the same line
*/
import java.util.Scanner;

public class Exercise_03_32 {
	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);	// Create Scanner object

		// 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(); 

		// Calculate point position
		double position = (x1 - x0) * (y2 - y0) - (x2 - x0) * (y1 - y0);

		// Display result
		System.out.print("(" + x2 + ", " + y2 + ") is on the ");
		if (position > 0)
			System.out.print("left side of the "); 
		if (position < 0)
			System.out.print("right side of the ");
		System.out.println("line from (" + x0 + ", " + y0 + 
			") to (" + x1 + ", " + y1 + ")");
	}
}