# Find if it’s possible to rotate the page by an angle or not.

• Difficulty Level : Easy
• Last Updated : 22 Jun, 2022

You are given three points a, b, c on a page. Find if it’s possible to rotate the page around the point by an angle, such that the new position of ‘a’ is same as the old position of ‘b’, and the new position of ‘b’ is same as the old position of ‘c’. If such angle exists print “Yes”, else “No”.
Examples:

```Input : a1 = 0, a2 = 1, b1 = 1, b2 =  1,
c1 = 1, c2 = 0
Output : Yes
Explanation : Rotate the page by 90 degree.

Input : a1 = 1, a2 = 1, b1 = 0, b2 = 0,
c1 = 1000, c2 = 1000
Output : No```

Recommended Practice

Rotation of page by some angle is only possible if the distance between points ‘a’ and ‘b’ is equal to distance between points ‘b’ and ‘c’. But if the points are on same line, there is no rotation at point ‘b’. The problem has no solution when ‘a’, ‘b’, ‘c’ are in the same line or dis(a, b) != dis(b, c)

## C++

 `// C++ program to find if its possible``// to rotate page or not``#include``using` `namespace` `std;` `// function to find if it's possible``// to rotate page or not``void` `possibleOrNot(``long` `long` `a1, ``long` `long` `a2,``                   ``long` `long` `b1, ``long` `long` `b2,``                   ``long` `long` `c1, ``long` `long` `c2){``    ` `    ``// Calculating distance b/w points``    ``long` `long` `dis1 = ``pow``(b1 - a1, 2) +``                      ``pow``(b2 - a2, 2);``    ``long` `long` `dis2 = ``pow``(c1 - b1, 2) +``                      ``pow``(c2 - b2, 2);` `    ``// If distance is not equal``    ``if``(dis1 != dis2)``        ``cout << ``"No"``;``        ` `    ``// If the points are in same line``    ``else` `if` `(b1 == ((a1 + c1) / 2.0) && b2 ==``                          ``((a2 + c2) / 2.0))``        ``cout << ``"No"``;``    ``else``        ``cout << ``"Yes"``;``}` `// Driver Code``int` `main()``{``    ``ios_base::sync_with_stdio(``false``);``    ``cin.tie(NULL);``    ` `    ``// Points a, b, and c``    ``long` `long` `a1 = 1, a2 = 0, b1 = 2,``             ``b2 = 0, c1 = 3, c2 = 0;``    ``possibleOrNot(a1, a2, b1, b2, c1, c2);``    ``return` `0;``}`

## Java

 `// java program to find if its possible``// to rotate page or not``import` `java.util.Arrays;` `class` `GFG {``        ` `    ``// function to find if it's possible``    ``// to rotate page or not``    ``static` `void` `possibleOrNot(``long` `a1,``long` `a2,``                              ``long` `b1,``long` `b2,``                              ``long` `c1,``long` `c2)``    ``{``        ` `        ``// Calculating distance b/w points``        ``long` `dis1 = (``long``)Math.pow(b1 - a1, ``2``) +``                    ``(``long``) Math.pow(b2 - a2, ``2``);``                    ` `        ``long` `dis2 = (``long``)Math.pow(c1 - b1, ``2``) +``                     ``(``long``)Math.pow(c2 - b2, ``2``);``    ` `        ``// If distance is not equal``        ``if``(dis1 != dis2)``            ``System.out.print(``"No"``);``            ` `        ``// If the points are in same line``        ``else` `if` `(b1 == ((a1 + c1) / ``2.0``) &&``                       ``b2 == ((a2 + c2) / ``2.0``))``            ``System.out.print(``"No"``);``        ``else``            ``System.out.print(``"Yes"``);``    ``}``    ` `    ``// Driver method``    ``public` `static` `void` `main(String[] args)``    ``{``        ` `        ``// Points a, b, and c``        ``long` `a1 = ``1``, a2 = ``0``, b1 = ``2``,``                ``b2 = ``0``, c1 = ``3``, c2 = ``0``;``                ` `        ``possibleOrNot(a1, a2, b1, b2, c1, c2);``    ``}``}` `// This code is contributed by Anant Agarwal.`

## Python3

 `# Python3 program to fill an``# array with frequencies.` `# Function to find if it's possible``# to rotate page or not``def` `possibleOrNot(a1, a2, b1, b2, c1, c2):``    ` `    ``# Calculating distance b/w points``    ``dis1 ``=` `(``pow``(b1 ``-` `a1, ``2``) ``+``            ``pow``(b2 ``-` `a2, ``2``))``    ``dis2 ``=` `(``pow``(c1 ``-` `b1, ``2``) ``+``            ``pow``(c2 ``-` `b2, ``2``))` `    ``# If distance is not equal``    ``if``(dis1 !``=` `dis2):``        ``print``(``"No"``)``        ` `    ``# If the points are in same line``    ``else` `if` `(b1 ``=``=` `((a1 ``+` `c1) ``/``/` `2.0``) ``and``          ``b2 ``=``=` `((a2 ``+` `c2) ``/``/` `2.0``)):``        ``print``(``"No"``)``    ``else``:``        ``print``(``"Yes"``)` `# Driver Code` `# Points a, b, and c``a1, b1, c1 ``=` `1``, ``2``, ``3``a2 ``=` `b2 ``=` `c2 ``=` `0``possibleOrNot(a1, a2, b1, b2, c1, c2)` `# This code is contributed by Anant Agarwal.`

## C#

 `// C# program to fill an array with frequencies.``using` `System;` `class` `GFG``{``    ``// function to find if it's possible``    ``// to rotate page or not``    ``static` `void` `possibleOrNot(``long` `a1,``long` `a2,``                              ``long` `b1,``long` `b2,``                              ``long` `c1,``long` `c2)``    ``{``         ` `        ``// Calculating distance b/w points``        ``long` `dis1 = (``long``)Math.Pow(b1 - a1, 2) +``                    ``(``long``) Math.Pow(b2 - a2, 2);``        ``long` `dis2 = (``long``)Math.Pow(c1 - b1, 2) +``                    ``(``long``)Math.Pow(c2 - b2, 2);``     ` `        ``// If distance is not equal``        ``if``(dis1 != dis2)``            ``Console.Write(``"No"``);``             ` `        ``// If the points are in same line``        ``else` `if` `(b1 == ((a1 + c1) / 2.0) && b2 ==``                       ``((a2 + c2) / 2.0))``            ``Console.Write(``"No"``);``        ``else``            ``Console.Write(``"Yes"``);``    ``}``    ` `    ``// Driver method``    ``public` `static` `void` `Main()``    ``{``        ``// Points a, b, and c``        ``long`  `a1 = 1, a2 = 0, b1 = 2,``                 ``b2 = 0, c1 = 3, c2 = 0;``        ``possibleOrNot(a1, a2, b1, b2, c1, c2);``    ``}``}``// This code is contributed by Anant Agarwal.`

## PHP

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## Javascript

 ``

Output:

`No`

Time Complexity: O(logn)

Auxiliary Space: O(1)

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