import math
import matplotlib.pyplot as plt

class Point:
    __x__ = 0.0
    __y__ = 0.0

    def __init__(self, x = 0.0, y = 0.0):
        self.__x__ = x
        self.__y__ = y

    def __str__(self):
        return f"({self.__x__:.3f},{self.__y__:.3f})"

    def __neg__(self):
        return Point(-self.__x__, -self.__y__)

    def __add__(self, other):
        if isinstance(other, Point):
            return Point(self.__x__ + other.__x__, self.__y__ + other.__y__)
        elif isinstance(other, int) or isinstance(other, float):
            return Point(self.__x__ + other, self.__y__ + other)
        else:
            raise ValueError("Operand must be Point, int or float.")

    def __radd__(self, other):
        return self + other

    def __sub__(self, other):
        return self + (-other)

    def __rsub__(self, other):
        return self - other

    def __mul__(self, other):
        if isinstance(other, Point):
            return Point(self.__x__ * other.__x__, self.__x__ * other.__y__)
        elif isinstance(other, int) or isinstance(other, float):
            return Point(self.__x__ * other, self.__x__ * other)
        else:
            raise ValueError("Operand must be Point, int or float.")

    def __rmul__(self, other):
        return self * other

    def rot(self, degree):
        x =  math.cos(degree) * self.__x__ + math.sin(degree) * self.__y__
        y =  -math.sin(degree) * self.__x__ + math.cos(degree) * self.__y__
        return Point(x, y)

    def get_x(self):
        return self.__x__

    def get_y(self):
        return self.__y__

p1 = Point()
p2 = Point(1, 1)
p3 = Point (3, 2)
p4 = 2 * p2 + p3 - 1
p5 = p4.rot(math.pi / 2)

plt.plot(p1.get_x(), p1.get_y(), "orange", marker = "o", label = p1)
plt.plot(p2.get_x(), p2.get_y(), "green", marker = "o", label = p2)
plt.plot(p3.get_x(), p3.get_y(), "yellow", marker = "o", label = p3)
plt.plot(p4.get_x(), p4.get_y(), "purple", marker = "o", label = 2 * p2 + p3 - 1)
plt.plot(p5.get_x(), p5.get_y(), "purple", marker = "o", label = f"{p4} rotated 90°")

plt.title("Points")
plt.xlabel("x")
plt.ylabel("y")
plt.legend()

plt.show()