Can three given coordinates be points of a rectangle

I am currently learning how to code in Python and I came across this task and I am trying to solve it. But I think I got a mistake somewhere and I was wondering can maybe someone help me with it. The task is to write a code that will: Import four 2D coordinates (A, B, C and X) from a text file Check can A, B, C be points of a rectangle Check if X is inside the ABC rectangle Calculate the diagonal of the rectangle.

So far I have this:

import math

def distance(point1, point2):
    return math.sqrt((point2[0] - point1[0])**2 + (point2[1] - point1[1])**2)

def is_rectangle(point1, point2, point3):
    distances = [
        distance(point1, point2),
        distance(point2, point3),
        distance(point3, point1)
    ]

    distances.sort()

    if distances[0] == distances[1] and distances[1] != distances[2]:
        return True
    else:
        return False
def is_inside_rectangle(rectangle, point):
    x_values = [vertex[0] for vertex in rectangle]
    y_values = [vertex[1] for vertex in rectangle]

    if (min(x_values) < point[0] < max(x_values)) and (min(y_values) < point[1] < max(y_values)):
        return True
    else:
        return False

with open('coordinates.txt', 'r') as file:
    coordinates = []
    for line in file:
        x, y = map(int, line.strip()[1:-1].split(','))
        coordinates.append((x, y))

rectangle = [coordinates[0], coordinates[1], coordinates[2]]
diagonal1 = distance(coordinates[0], coordinates[2])
diagonal2 = distance(coordinates[1], coordinates[3])
if is_rectangle(coordinates[0], coordinates[1], coordinates[2]) and is_inside_rectangle(rectangle, coordinates[3]):
    print("True")
    print(f"Diagonal of the rectangle is: {max(diagonal1, diagonal2)}")

else:
    print("False")

The code works but I think it calculates the diagonal wrong. For example lets take this points for input: A(0, 0), B(5,0), C(0, 5) and X(2, 2). It says they can be points of a rectangle and that the diagonal is 5. When I put this points on paper, the fourth point can be D(5, 5) and then the diagonal is 7.07 (square root of 50). Or it can be D(-5, 5) but then it is a parallelogram and one diagonal is 5 but it is not the max one. Also I am trying to write a function that will check if all data in the text file are integers. Let's say B is (m, k), then it should return false and if all data are integers, then continue with the code. Any ideas on that one?

Solution

Let's look at the logic for your is_rectangle function.

def is_rectangle(point1, point2, point3):
    distances = [
        distance(point1, point2),
        distance(point2, point3),
        distance(point3, point1)
    ]

    distances.sort()

    if distances[0] == distances[1] and distances[1] != distances[2]:
        return True
    else:
        return False

You are testing if the two smallest sides of triangle ABC are equal, and different from the largest side.

Effectively answering the question: "Is ABC an obtuse isosceles triangle?"

But the question you should be asking is: "Is ABC a right triangle?"

There are several ways to test whether a triangle ABC is a right triangle.

One way is to check if one of the three pairs of vectors (AB,AC), (BA,BC), (CA, CB) is orthogonal, ie if its dot product is 0.
Another way is to check if the three distances AB, AC, BC form a Pythagorean triplet, ie if z**2 == x**2 + y**2 is true when x,y,z = sorted(map(distance,itertools.combinations(points,2)))

PS: In general when you write if condition: return True else: return False, you might as well write directly return condition.

With that in mind, the code you wrote in python for this function is equivalent to:

from itertools import combinations

def is_acute_isosceles_triangle(point1, point2, point3):
    distances = sorted(map(distance, combinations((point1,point2,point3), 2)))
    return (distances[0] == distances[1] and distances[1] != distances[2])