Reflection of a point at 180 degree rotation of another point

Given two points coordinates (x₁, y₁) and (x₂, y₂)on 2D plane. The task is to find the reflection of (x₁, y₁) at 180 degree rotation of (x₂, y₂).
Examples:

Input : x1 = 0, y1 = 0, x2 = 1, y2 = 1
Output : (2, 2)

Input : x1 = 1, y1 = 1, x2 = 2, y2 = 2
Output : (3, 3)

Let the reflection point of point (x₁, y₁) about (x₂, y₂) be (x’, y’). 
For (x’, y’) be the 180 degree rotation of point (x₁, y₁) around point (x₂, y₂), they all must be collinear i.e all the three point must lie on a same straight line. Also, observe (x₂, y₂) will became mid point between (x₁, y₁) and (x’, y’). 

So, 
x’ – x₂ = x₂ – x₁
y’ – y₂ = y₂ – y₁
x’ = 2 * x₂ – x₁
y’ = 2 * y₂ – y₁
Below is the implementation of this approach: 

C++

// CPP Program to find the 180 degree reflection
// of one point around another point.
#include <bits/stdc++.h>
using namespace std;

void findPoint(int x1, int y1, int x2, int y2)
{
    cout << "(" << 2 * x2 - x1 << ", "
         << 2 * y2 - y1 << ")";
}


int main()
{
    int x1 = 0, y1 = 0, x2 = 1, y2 = 1;
    findPoint(x1, y1, x2, y2);
    return 0;
}

Java

// Java Program to find the 180 degree
// reflection of one point around
// another point.
class GFG {

    static void findPoint(int x1, int y1,
                          int x2, int y2)
    {
        System.out.println("(" + (int)(2 * x2 - x1)
               + "," + (int)(2 * y2 - y1 ) + " )");
    }

    // Driver code
    public static void main(String args[])
    {
        int x1 = 0, y1 = 0, x2 = 1, y2 = 1;

        findPoint(x1, y1, x2, y2);
    }
}

// This code is contributed by Arnab Kundu.

Python3

# Python3 Program for find the 180
# degree reflection of one point
# around another point.

def findPoint(x1, y1, x2, y2):
    print("(" , 2 * x2 - x1 , ",",
                2 * y2 - y1 ,")");

# Driver Code
x1 = 0;
y1 = 0;
x2 = 1;
y2 = 1;
findPoint(x1, y1, x2, y2);

# This code is contributed by mits

C#

// C# Program to find the 180 degree reflection
// of one point around another point.
using System;

public class GFG {

    static void findPoint(int x1, int y1,
                          int x2, int y2)
    {
        Console.WriteLine("(" + (int)(2 * x2 - x1)
               + "," + (int)(2 * y2 - y1 ) + " )");
    }

    // Driver code
    static public void Main(String []args)
    {
        int x1 = 0, y1 = 0, x2 = 1, y2 = 1;

        findPoint(x1, y1, x2, y2);
    }
}

// This code is contributed by Arnab Kundu.

PHP

<?php
// PHP Program for find the 180
// degree reflection of one point
// around another point.

function findPoint($x1, $y1, $x2, $y2)
{
    echo "(" , 2 * $x2 - $x1 , ", "
                , 2 * $y2 - $y1 ,")";
}

    // Driver Code
    $x1 = 0;
    $y1 = 0;
    $x2 = 1;
    $y2 = 1;
    findPoint($x1, $y1, $x2, $y2);

// This code is contributed by anuj_67
?>

Javascript

<script>

// Javascript Program to find the 180 degree reflection
// of one point around another point.

function findPoint(x1, y1, x2, y2)
{
    document.write("(" + 2 * (x2 - x1) + ", "
        + 2 * (y2 - y1) + ")");
}

    let x1 = 0, y1 = 0, x2 = 1, y2 = 1;
    findPoint(x1, y1, x2, y2);


// This code is contributed by Mayank Tyagi

</script>

Output:

(2, 2)

Time Complexity : O(1)

Space Complexity : O(1) since using constant variables