Find all possible coordinates of a parallelogram in Java

A parallelogram is a quadrilateral with two pairs of parallel sides, where the opposite sides are equal in length and the diagonals are equal in measure.

In this article we are going to find all possible coordinates of a Parallelogram.

Basically, we will find all the possible coordinates from the given three coordinates to make a parallelogram of a non-zero area. Here the three given coordinates are not fixed points and can change.

Thus, if three coordinates are given, we can assert that only these three coordinates can construct a parallelogram.

As per diagram given above, the opposite sides of a parallelogram are equal in length i.e., AD = BC and AB = CD, we can calculate the coordinates of the missing point (D) as

AD = BC

(Dx - Ax, Dy - Ay) = (Cx - Bx, Cy - By)

Dx = Ax Cx - Bx

Dy = Ay Cy - By

let's start!

Show you some examples

Instance-1

Suppose these three points are −

{a1 = 3, a2 = 2}, {b1 = 1, b2 = 0}, {c1 = 4, c2 = 2}

After finding all possible coordinates of a Parallelogram, result will be −

The (x, y) coordinates are −

0, 0

6, 4

2, 0

Instance-2

Suppose these three points are −

{a1 = 7, a2 = 2}, {b1 = 3, b2 = 0}, {c1 =0, c2 = 1}

After finding all possible coordinates of a Parallelogram, result will be −

The (x,y) coordinates are −

10, 1

4, 3

-4, -1

Algorithm

Step 1 − Declare the three coordinates of parallelogram.

Step 2 − Find the other possible coordinates using the formula.

Step 3 − Print the result.

Multiple Approaches

We provide solutions in different ways.

• By using static input values

• By user-defined method

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

Method 1: By using static input values

In this method, we will take these three points as static input and apply the formula to print the result.

Example

public class Main{

   // main method
   public static void main(String[] args){

      //Declare the three coordinates of parallelogram
      int a1 = 3, a2 = 2;
      int b1 = 1, b2 = 0;
      int c1 = 4, c2 = 2;
       
      //find the other possible coordinates and printing it
      System.out.println("The (x,y) coordinates are: ");
      System.out.println(a1 + b1 - c1 + ", " + (a2 + b2 - c2));
      System.out.println(a1 + c1 - b1 + ", " + (a2 + c2 - b2));
      System.out.println(c1 + b1 - a1 + ", " + (c2 + b2 - a2));
   }
}

Output

The (x,y) coordinates are: 
0, 0
6, 4
2, 0

Approach-2: By Using User Defined Method

In this approach, first we will initialise a user defined method and we will take the three points as input and apply the formula to print the result.

Example

public class Main {
	
   // main method
   public static void main(String[] s){
      //Declare the three coordinates of parallelogram 
      int a1 = 7, a2 = 2; 
      int b1 = 3, b2 = 0; 
      int c1 = 0, c2 = 1; 
      //calling user defined function
      func(a1, a2, b1, b2, c1, c2);
   }
      
   //user defined function
   static void func(int a1, int a2, int b1, int b2, int c1, int c2){
      //find the other possible coordinates and printing it
      System.out.println("The (x,y) coordinates are: ");
      System.out.println(a1 + b1 - c1 + ", " + (a2 + b2 - c2));
      System.out.println(a1 + c1 - b1 + ", " + (a2 + c2 - b2));
      System.out.println(c1 + b1 - a1 + ", " + (c2 + b2 - a2));
   }
}

Output

The (x,y) coordinates are: 
10, 1
4, 3
-4, -1

In this article, we explored how to find all possible coordinates of a parallelogram in Java by using different methods.

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