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

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: Please try your approach on {IDE} first, before moving on to the solution.

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){            // Calulating 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)     {                    // Calulating 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.

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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):            # Calulating 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     elif (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)     {                     // Calulating 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.



Output:

No