Two points on line 1 are given as (x1, y1) and (x2, y2) and on line 2 as (x3, y3

Question

Two points on line 1 are given as (x1, y1) and (x2, y2) and on line 2 as (x3, y3) and (x4, y4), as shown in Figure 3.8a-b. The intersecting point of the two lines can be found by solving the following linear equation: (y1-y2)x - (x1 - x2)y = (y1 - y2)x1 - (x1 - x2)y1 (y3 - y4)x - (x3 - x4)y = (y3 - y4)x3 - (x3 - x4)y3 This linear equation can be solved using Cramer's rule (see Programming Exercise 3.3). If the equation has no solutions, the two lines are parallel (Figure 3.8c). Write a program that prompts the user to enter four points and displays the intersecting point. Here are sample runs:

Explanation / Answer

import javax.swing.JOptionPane;

class MyExample {

private static double x1;

private static double x2;

private static double x3;

private static double x4;

private static double y1;

private static double y2;

private static double y3;

private static double y4;

private static double intersectionp;

public static void main(String[] args) {
   MyExample p=new MyExample();
   p.intersection();
}

public void intersection(){

String userInputx1 = JOptionPane.showInputDialog("Enter the first x cordinate of the first line:");

// System.out.println(userInputx1); //to test if working

x1 = Double.parseDouble(userInputx1);

String userInputx2 = JOptionPane.showInputDialog("Enter the second x cordinate of the first line:");

x2 = Double.parseDouble(userInputx2);

String userInputx3 = JOptionPane.showInputDialog("Enter the first x cordinate of the second line:");

x3 = Double.parseDouble(userInputx3);

String userInputx4 = JOptionPane.showInputDialog("Enter the second x cordinate of the second line:");

x4 = Double.parseDouble(userInputx4);

String userInputy1 = JOptionPane.showInputDialog("Enter the first y cordinate of the first line:");

y1 = Double.parseDouble(userInputy1);

String userInputy2 = JOptionPane.showInputDialog("Enter the second y cordinate of the first line:");

y2 = Double.parseDouble(userInputy2);

String userInputy3 = JOptionPane.showInputDialog("Enter the first y cordinate of the second line:");

y3 = Double.parseDouble(userInputy3);

String userInputy4 = JOptionPane.showInputDialog("Enter the second y cordinate of the second line:");

y4 = Double.parseDouble(userInputy4);

double d = (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4);

if (d == 0) System.out.println("Parallel");;

double xi = ((x3-x4)*(x1*y2-y1*x2)-(x1-x2)*(x3*y4-y3*x4))/d;

double yi = ((y3-y4)*(x1*y2-y1*x2)-(y1-y2)*(x3*y4-y3*x4))/d;

System.out.println(intersectionp);

// return new Point(xi,yi);

}

}

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