Create a Rectangle class. This class stores only the Cartesian coordinates of the four corners of the rectangle. The constructor calls a set function that accepts four sets of coordinates and verifies that each of these is in the first quadrant with no single x- or y-coordinate larger than 20.0. The set function also verifies that the supplied coordinates do, in fact, specify a rectangle. Provide member functions that calculate the length, width, perimeter and area. The length is the larger of the two dimensions. Include a predicate function square that determines whether the rectangle is a square

Sure, I can help you with that! Here is a possible implementation of the Rectangle class in Python:

class Rectangle:
    def __init__(self, x1, y1, x2, y2, x3, y3, x4, y4):
        self.set_coordinates(x1, y1, x2, y2, x3, y3, x4, y4)

    def set_coordinates(self, x1, y1, x2, y2, x3, y3, x4, y4):
        # Verify that all coordinates are in the first quadrant
        if x1 < 0 or y1 < 0 or x2 < 0 or y2 < 0 or x3 < 0 or y3 < 0 or x4 < 0 or y4 < 0:
            raise ValueError("All coordinates must be in the first quadrant")
        # Verify that no coordinate is larger than 20.0
        if x1 > 20.0 or y1 > 20.0 or x2 > 20.0 or y2 > 20.0 or x3 > 20.0 or y3 > 20.0 or x4 > 20.0 or y4 > 20.0:
            raise ValueError("No coordinate can be larger than 20.0")
        # Verify that the coordinates specify a rectangle
        if not self.is_rectangle(x1, y1, x2, y2, x3, y3, x4, y4):
            raise ValueError("The coordinates do not specify a rectangle")
        # Store the coordinates as a list of tuples
        self.coordinates = [(x1, y1), (x2, y2), (x3, y3), (x4, y4)]

    def is_rectangle(self, x1, y1, x2, y2, x3, y3, x4, y4):
        # Check if the four sides have equal length and opposite sides are parallel
        return self.distance(x1, y1, x2, y2) == self.distance(x3, y3, x4, y4) and \
               self.distance(x2, y2, x3, y3) == self.distance(x4, y4, x1, y1) and \
               abs((y2 - y1) * (y4 - y3) + (x2 - x1) * (x4 - x3)) < 1e-10

    def distance(self, x1, y1, x2, y2):
        # Calculate the distance between two points
        return ((x2 - x1) ** 2 + (y2 - y1) ** 2) ** 0.5

    def length(self):
        # Calculate the length of the rectangle (longer dimension)
        return max(self.distance(self.coordinates[0][0], self.coordinates[0][1],
                                  self.coordinates[1][0], self.coordinates[1][1]),
                   self.distance(self.coordinates[1][0], self.coordinates[1][1],
                                  self.coordinates[2][0], self.coordinates[2][1]))

    def width(self):
        # Calculate the width of the rectangle (shorter dimension)
        return min(self.distance(self.coordinates[0][0], self.coordinates[0][1],
                                  self.coordinates[1][0], self.coordinates[1][1]),
                   self.distance(self.coordinates[1][0], self.coordinates[1][1],
                                  self.coordinates[2][0], self.coordinates[2][1]))

    def area(self):
        # Calculate the area of the rectangle
        return self.length() * self.width()

    def perimeter(self):
        # Calculate the perimeter of the rectangle
        return 2 * self.length() + 2 * self.width()

    def is_square(self):
        # Check if the rectangle is a square (equal length and width)
        return abs(self.length() - self.width()) < 1e-10

Here is an example of how to use this class:

# Create a rectangle with coordinates (0, 0), (0, 5), (10, 5), (10, 0)
rect = Rectangle(0, 0, 0, 5, 10, 5, 10, 0)

# Print the length, width, area, perimeter, and whether it's a square
print(rect.length())    # Output: 10.0
print(rect.width())     # Output: 5.0
print(rect.area())      # Output: 50.0
print(rect.perimeter()) # Output: 30.0
print(rect.is_square()) # Output: False