(Geometry: intersecting point) Suppose two line segments intersect. The two end-points for the first line segment are (x1, y1) and (x2, y2) and for the second line segment are (x3, y3) and (x4, y4).Write a program that prompts the user to enter these four endpoints and displays the intersecting point. the intersecting point can be found by solving a linear equation. Write the LinearEquation class in Programming to solve this equation. input style : Enter eight double number output style: Displays the intersecting point or The two lines are parallel

Here's one possible solution in Java:

import java.util.Scanner;

public class IntersectingPoint {
    public static void main(String[] args) {
        // Prompt the user to enter the four endpoints
        Scanner input = new Scanner(System.in);
        System.out.print("Enter x1, y1, x2, y2, x3, y3, x4, y4: ");
        double x1 = input.nextDouble();
        double y1 = input.nextDouble();
        double x2 = input.nextDouble();
        double y2 = input.nextDouble();
        double x3 = input.nextDouble();
        double y3 = input.nextDouble();
        double x4 = input.nextDouble();
        double y4 = input.nextDouble();
        
        // Create two LinearEquation objects for the two line segments
        LinearEquation eq1 = new LinearEquation(y1 - y2, x2 - x1, y1*x2 - y2*x1);
        LinearEquation eq2 = new LinearEquation(y3 - y4, x4 - x3, y3*x4 - y4*x3);
        
        // Check if the two lines are parallel
        if (eq1.isParallel(eq2)) {
            System.out.println("The two lines are parallel");
        } else {
            // Compute the intersecting point
            double x = eq1.getX(eq2);
            double y = eq1.getY(eq2);
            System.out.printf("The intersecting point is (%.2f, %.2f)\n", x, y);
        }
    }
}

class LinearEquation {
    private double a, b, c;

    public LinearEquation(double a, double b, double c) {
        this.a = a;
        this.b = b;
        this.c = c;
    }

    public double getA() {
        return a;
    }

    public double getB() {
        return b;
    }

    public double getC() {
        return c;
    }

    public boolean isParallel(LinearEquation other) {
        return Math.abs(a * other.b - b * other.a) < 1e-6;
    }

    public double getX(LinearEquation other) {
        return (c * other.b - b * other.c) / (a * other.b - b * other.a);
    }

    public double getY(LinearEquation other) {
        return (a * other.c - c * other.a) / (a * other.b - b * other.a);
    }
}

The program first prompts the user to enter the four endpoints, then creates two `LinearEquation` objects for the two line segments, and finally checks if the two lines are parallel or computes the intersecting point using the `getX` and `getY` methods of the `LinearEquation` class. The `isParallel` method checks if the two lines are parallel by comparing the slopes of the two lines, and the `getX` and `getY` methods solve the system of two linear equations for the intersecting point.