Check if 4 points form a Square Python

 PROGRAM TO CHECK IF FOUR POINTS FORM A SQUARE




class Point:

      

    # Structure of a point in 2D space

    def __init__(self, x, y):

        self.x = x

        self.y = y

  

# A utility function to find square of 

# distance from point 'p' to point 'q'

def distSq(p, q):

    return (p.x - q.x) * (p.x - q.x) +\

           (p.y - q.y) * (p.y - q.y)

  

# This function returns true if (p1, p2, p3, p4) 

# form a square, otherwise false

def isSquare(p1, p2, p3, p4):

  

    d2 = distSq(p1, p2) # from p1 to p2

    d3 = distSq(p1, p3) # from p1 to p3

    d4 = distSq(p1, p4) # from p1 to p4

  

    if d2 == 0 or d3 == 0 or d4 == 0:    

        return False

  

    # If lengths if (p1, p2) and (p1, p3) are same, then

    # following conditions must be met to form a square.

    # 1) Square of length of (p1, p4) is same as twice

    # the square of (p1, p2)

    # 2) Square of length of (p2, p3) is same

    # as twice the square of (p2, p4)

  

    if d2 == d3 and 2 * d2 == d4 and \

                    2 * distSq(p2, p4) == distSq(p2, p3):

        return True

  

    # The below two cases are similar to above case

    if d3 == d4 and 2 * d3 == d2 and \

                    2 * distSq(p3, p2) == distSq(p3, p4):

        return True

  

    if d2 == d4 and 2 * d2 == d3 and \

                    2 * distSq(p2, p3) == distSq(p2, p4):

        return True

  

    return False

  

# Driver Code

if __name__=="__main__":

    p1 = Point(20, 10)

    p2 = Point(10, 20)

    p3 = Point(20, 20)

    p4 = Point(10, 10)

      

    if isSquare(p1, p2, p3, p4):

        print('Yes') 

    else:

        print('No')

  

OUTPUT

Yes

CREDITS: https://www.geeksforgeeks.org/check-given-four-points-form-square/