Это квадрат?

data = [(0, 0), (0, 1), (1, 0), (1, 1)]
print(is_it_square(*data))

data = [(0, 0), (0, 1), (1, 0), (1, -1)]
print(is_it_square(*data))

from math import isqrt
data = [(0, 0), (0, 1), (1, 0), (1, 1)]
#data = [(0, 0), (0, 1), (1, 0), (1, -1)]
def is_it_square(*data):
    dst_sq=lambda p,q: (p[0]-q[0])**2+(p[1]-q[1])**2
    d=sorted([dst_sq(data[i], data[j]) for i in range(4) for j in range(i) ])
    if all(2*d[i]==d[-1] if i<4 else d[i]==d[-1] for i in d):
        return isqrt(d[0])
print(is_it_square(*data))

from collections import Counter
from itertools import combinations
 
def square_distance(p1,p2):
    return (p1[0]-p2[0])**2 + (p1[1]-p2[1])**2
 
def is_it_square(*data):
    cnt = Counter([square_distance(x, y) for x, y in combinations(data, 2)])
    if len(cnt)==2:
        for i, v in cnt.items(): 
            if v == 4: return int(i**0.5)

from math import isqrt
#data = [(0, 0), (0, 1), (1, 0), (1, 1)]
data = [(0, 0), (3,4), (-1, 7), (-4, 3)]
def is_it_square(*data):
    dst_sq=lambda p,q: (p[0]-q[0])**2+(p[1]-q[1])**2
    d=sorted([dst_sq(data[i], data[j]) for i in range(4) for j in range(i) ])
    if all(2*d[i]==d[-1] if i<4 else d[i]==d[-1] for i in range(6)):
        return isqrt(d[0])
print(is_it_square(*data))

def dist(v1,v2):
    return (v1[0]-v2[0])**2+(v1[1]-v2[1])**2
    
def check_square(v1,v2,v3,v4):
    
    d=[]
    
    d.append(dist(v1,v2))
    d.append(dist(v1,v3))
    d.append(dist(v1,v4))
    d.append(dist(v2,v3))
    d.append(dist(v2,v4))
    d.append(dist(v3,v4))
    
    d.sort()
    
    max_d=max(d)
    min_d=min(d)
    
    max_count=d.count(max_d)
    min_count=d.count(min_d)
    
    return (min_count == 4) and (max_count == 2) and (max_d == 2*min_d)
    
print(check_square((0,0),(0,1),(1,0),(1,1)))

def get_segment_length_sqr(begin_cord: tuple[float], end_cord: tuple[float]) -> float:
    """Квадрат отрезока из коодинат точек"""
    return (end_cord[0] - begin_cord[0]) ** 2 + (end_cord[1] - begin_cord[1]) ** 2
 
 
def get_diagonal_sqr(segmt_sqr1: float, segmt_sqr2: float) -> float:
    """Квадрат диагонали из сторон"""
    return segmt_sqr1 + segmt_sqr2
 
 
def is_it_square(diagonal_sqr1: float, diagonal_sqr2: float, epsilon=1.e-6) -> bool:
    return abs(diagonal_sqr1 - diagonal_sqr2) < epsilon
 
# координаты фигуры фундамента задаются напрерывно, по часовой стрелке
data: list[tuple] = [(0, 0), (0, 1), (1, 1), (1, 0)] 
s1 = get_segment_length_sqr(data[0], data[1])
s2 = get_segment_length_sqr(data[1], data[2])
s3 = get_segment_length_sqr(data[2], data[3])
s4 = get_segment_length_sqr(data[3], data[0])
 
d1 = get_diagonal_sqr(s1, s2)  # 1-я диагональ квадрата 
d2 = get_diagonal_sqr(s1, s4)  # 2-я диагональ квадрата
 
print(is_it_square(d1, d2))