# 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:

 `// CPP Program tof find the 180 degree reflection ` `// of one point around another point. ` `#include ` `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 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 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# 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. `

 ` `

Output:
```(2, 2)
```

Time Complexity : O(1)

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