How to confirm in Java whether given four points form a square?

A square is a two-dimensional shape with four sides of equal length. Opposite sides of a square are parallel, all four interior angles are right angles, and the diagonals are of equal length. In this article we will examine how to confirm whether a given four points form a square.

We will get a square with four points, namely A, B, C, D, as shown in the figure −

We need to check from these points whether they form a square. In order to check this, it should satisfy the following conditions −

• The distance between point A and point C, and the distance between point B and point D i.e. "x" should be equal.

• The distance between point A and point B, the distance between point B and point C, the distance between point C and point D, the distance between point D and point A i.e. "z" should equal.

We will find the distance between two points using the formula -

$$\mathrm{d=\sqrt{(x_{2}-x_{1})^2(y_{2}-y_{1})^2}}$$

Point 1 will be (x1, y1), point 2 will be (x2, y2).

let's start!

Show you some examples

The Chinese translation of

Instance-1

is:

Instance-1

• Given four input points are -

• P1(3,7), P2(4,3), P3(7,8), P4(1,9)

• Put it into the distance formula and check if the square condition is met, the result will be -

• The given four points do not form a square.

Example-2

• Given four input points are -

• P1(20,20), P2(20,10), P3(10,10), P4(10,20)

• Put it into the distance formula and check if the square condition is met, the result will be -

• Given four points form a square.

algorithm

• Step-1 − Declare and initialize variables.

• Step-2 − Find the distance between center 1 and center 2 of the circle.

• Step 3 - Check the five distance conditions.

• Step-4 − Print the results.

Multiple methods

We provide solutions in different ways.

• By using static input

• By using user-defined methods

Let's look at the program and its output one by one.

Method 1: Use static input

In this method, point values ​​are assigned. Then according to the algorithm we will find out whether the given four points form a square.

The Chinese translation of

Example

is:

Example

public class Main{
   
   //main method
   public static void main(String[] args){
      
      //declaring variables
      int x1=3, x2=4, x3=7, x4=1;
      int y1=7, y2=3, y3=8, y4=9;
      double d1, d2, d3, d4, d5, d6;

      //applyinng logic
      d1 = (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
      d2 = (x3 - x2) * (x3 - x2) + (y3 - y2) * (y3 - y2);
      d3 = (x4 - x3) * (x4 - x3) + (y4 - y3) * (y4 - y3);
      d4 = (x1 - x4) * (x1 - x4) + (y1 - y4) * (y1 - y4);
	   d5 = (x4 - x2) * (x4 - x2) + (y4 - y2) * (y4 - y2);
      d6 = (x3 - x1) * (x3 - x1) + (y3 - y1) * (y3 - y1);  
      
      if (d1 == 0 || d2 == 0 || d3 == 0 || d4 == 0 || d5 == 0 || d6 == 0){
		   System.out.println("Given four points do not form a square");
      }
      else if (d1 == d2 && d2 == d3 && d3 == d4 && d5 == d6){
	      
         //prints if four points form square
	      System.out.println("Given four points form a square");
	   } else {
	      
         //prints if four points do not form square 
	      System.out.println("Given four points do not form a square");
	   }

	}
} 

Output

Given four points do not form a square

Method 2: Use user-defined methods

In this method, point values ​​are assigned. Then a user-defined method is called by passing the given value and based on the algorithm it determines whether the given four points form a square.

The Chinese translation of

Example

is:

Example

public class Main{

   //main method
   public static void main(String[] args){
   
      //creating objects of Point
      Point p1 = new Point(20, 20);
      Point p2 = new Point( 20, 10 );
      Point p3 = new Point(10, 10 );
      Point p4 = new Point( 10, 20 );

      //calling user defined method
      if(isSquare(p1, p2, p3, p4)==true){
      
         //print if four points form a square
         System.out.println("Given four points form a square");   
      }
      else{
         
         //print if points does not form a square
         System.out.println("Given four points do not form a square"); 
      }
   }

   // Declaring Point class
   static class Point{
      int x, y;
      public Point(int x, int y){
         this.x = x;
         this.y = y;
      }
   };

   //function to find square of distance from point 'p' to point 'q'
   static int distSq(Point p, Point q){
      return (p.x - q.x) * (p.x - q.x) + (p.y - q.y) * (p.y - q.y);
   }

   //user defined method
   static boolean isSquare(Point p1, Point p2, Point p3, Point p4){
      int d1 = distSq(p1, p2); 
      int d2 = distSq(p2, p3); 
      int d3 = distSq(p3, p4);
      int d4 = distSq(p4, p1);
	
      int d5 = distSq(p1, p3);
      int d6 = distSq(p2, p4);
      if (d1 == 0 || d2 == 0 || d3 == 0 || d4 == 0 || d5 == 0 || d6 == 0)
         return false;

      if (d1 == d2 && d2 == d3 && d3 == d4 && d5 == d6){
	   
         //it returns true if (p1, p2, p3, p4) form a square
         return true;
      }

      //it returns false if (p1, p2, p3, p4) do not form a square
      return false;
   }
}

Output

Given four points form a square

In this article, we explored different ways to check if a line touches, intersects, or lies outside a circle using the Java programming language.

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