ISC Practicals and Theory - Point Distance

A point on the plane is given by two coordinates, $(x, y)$. This program defines a class Point whose objects hold such a point, and finds the distance between two points and their midpoint. This is the single-class version: a default constructor, an accept() method that reads a point, and a method distance(Point p) that receives the other point as an object.

Definition

The distance between $P_1(x_1, y_1)$ and $P_2(x_2, y_2)$ is

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

The midpoint of the line joining them is

$M = \left(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\right)$

For example, for $(0, 0)$ and $(3, 4)$: $d = \sqrt{9 + 16} = 5$ and $M = (1.5, 2)$.

Algorithm

1. main creates two objects p1 and p2 of the class Point. The default constructor sets both to $(0, 0)$.
2. main calls p1.accept("point 1") and p2.accept("point 2"); each reads x and y with a Scanner.
3. main calls display() on each object to print the points.
4. main calls p1.distance(p2):
   • it finds dx = p.x - x and dy = p.y - y;
   • it returns Math.sqrt(dx * dx + dy * dy). The squares are made by multiplication, not Math.pow.
5. main prints the distance with printf("%.2f"), which gives 2 decimal places.
6. main calls p1.midpoint(p2), which finds the average of the x-coordinates and of the y-coordinates and prints the point.

Program

Each method does one job: accept() reads, distance() calculates, midpoint() prints the midpoint and display() prints a point. The point p passed to distance() and midpoint() is an object, so its data members are read with p.x and p.y.

import java.util.Scanner;

/**
 * Class Point stores a point (x, y) of the plane and finds the distance
 * and the midpoint between two points. Main version: default constructor,
 * accept() reads the point, and the methods take the other Point object.
 */
public class Point
{
    double x;   // x-coordinate of the point
    double y;   // y-coordinate of the point

    /**
     * Default constructor: places the point at the origin (0, 0).
     */
    Point()
    {
        x = 0;
        y = 0;
    }

    /**
     * Reads the x and y coordinates of this point from the keyboard.
     * Parameter: name - label of the point shown in the prompt.
     */
    void accept(String name)
    {
        Scanner sc = new Scanner(System.in);
        System.out.print("Enter x of " + name + ": ");
        x = sc.nextDouble();
        System.out.print("Enter y of " + name + ": ");
        y = sc.nextDouble();
    }

    /**
     * Finds the distance between this point and the point p
     * using sqrt((x2 - x1)^2 + (y2 - y1)^2).
     * Parameter: p - the other Point object.
     * Returns: the distance as a double.
     */
    double distance(Point p)
    {
        double dx = p.x - x;    // difference of the x-coordinates
        double dy = p.y - y;    // difference of the y-coordinates
        return Math.sqrt(dx * dx + dy * dy);   // squares by multiplication
    }

    /**
     * Prints the midpoint of this point and the point p.
     * Parameter: p - the other Point object. Returns nothing.
     */
    void midpoint(Point p)
    {
        double mx = (x + p.x) / 2;   // x-coordinate of the midpoint
        double my = (y + p.y) / 2;   // y-coordinate of the midpoint
        System.out.printf("Midpoint = (%.2f, %.2f)%n", mx, my);
    }

    /**
     * Displays this point, with 2 decimal places, as (x, y).
     */
    void display()
    {
        System.out.printf("(%.2f, %.2f)%n", x, y);
    }

    /**
     * Creates two Point objects, reads them and prints the results.
     */
    public static void main(String args[])
    {
        Point p1 = new Point();   // first point
        Point p2 = new Point();   // second point
        p1.accept("point 1");
        p2.accept("point 2");
        System.out.print("Point 1 = ");
        p1.display();
        System.out.print("Point 2 = ");
        p2.display();
        System.out.printf("Distance = %.2f%n", p1.distance(p2));
        p1.midpoint(p2);
    }
}

Variable description table

Sample input and output

Enter x of point 1: 0
Enter y of point 1: 0
Enter x of point 2: 3
Enter y of point 2: 4
Point 1 = (0.00, 0.00)
Point 2 = (3.00, 4.00)
Distance = 5.00
Midpoint = (1.50, 2.00)

Enter x of point 1: 2
Enter y of point 1: 2
Enter x of point 2: 2
Enter y of point 2: 2
Point 1 = (2.00, 2.00)
Point 2 = (2.00, 2.00)
Distance = 0.00
Midpoint = (2.00, 2.00)

Enter x of point 1: -1
Enter y of point 1: -1
Enter x of point 2: 2
Enter y of point 2: 3
Point 1 = (-1.00, -1.00)
Point 2 = (2.00, 3.00)
Distance = 5.00
Midpoint = (0.50, 1.00)

Enter x of point 1: 1.5
Enter y of point 1: -2
Enter x of point 2: -3.5
Enter y of point 2: 4
Point 1 = (1.50, -2.00)
Point 2 = (-3.50, 4.00)
Distance = 7.81
Midpoint = (-1.00, 1.00)

Dry run

Take the input $(-1, -1)$ and $(2, 3)$. Here p1 is $(-1, -1)$, p2 is $(2, 3)$, and distance() is called as p1.distance(p2).

The program prints Distance = 5.00 and Midpoint = (0.50, 1.00), as in the third sample run.

Variations

1. Triangle area "Write a program using the class Point to find the area of a triangle given three points."
2. Collinear points "Write a program to check whether three given points lie on one straight line."
3. Perimeter "Find the perimeter of a triangle whose vertices are three Point objects."