def shrink_points(points, center, factor):
    """
    Shrinks a set of 2D points around a given center.

    Args:
        points (list): List of 2D points represented as tuples (x, y).
        center (tuple): The center point (x, y) around which the points should be shrunk.
        factor (float): Shrink factor. A factor of 0.5 will shrink the points by half, 2 will double the distance, etc.

    Returns:
        list: A list of the shrunk 2D points as tuples (x, y).
    """
    if factor <= 0:
        raise ValueError("Shrink factor must be greater than 0")

    shrunk_points = []
    for point in points:
        x = center[0] + (point[0] - center[0]) * factor
        y = center[1] + (point[1] - center[1]) * factor
        shrunk_points.append((x, y))

    return shrunk_points

# Example usage:
points = [(2, 2), (4, 4), (6, 2), (4, 0)]
center = (4, 2)
factor = 0.5

shrunk_points = shrink_points(points, center, factor)
print(shrunk_points)

import matplotlib.pyplot as plt

def plot_points(original_points, shrunk_points, center):
    """
    Plots original and shrunk points using matplotlib.

    Args:
        original_points (list): List of original 2D points represented as tuples (x, y).
        shrunk_points (list): List of shrunk 2D points represented as tuples (x, y).
        center (tuple): The center point (x, y) around which the points were shrunk.
    """
    original_x, original_y = zip(*original_points)
    shrunk_x, shrunk_y = zip(*shrunk_points)

    plt.scatter(original_x, original_y, c='red', label='Original Points')
    plt.scatter(shrunk_x, shrunk_y, c='blue', label='Shrunk Points')
    plt.scatter(center[0], center[1], c='green', marker='x', label='Center')

    plt.legend()
    plt.xlabel('x')
    plt.ylabel('y')
    plt.title('Shrinking Points Around a Center')

    plt.show()

# Example usage:
points = [(2, 2), (4, 4), (6, 2), (4, 0)]
center = (4, 2)
factor = 0.5

shrunk_points = shrink_points(points, center, factor)
plot_points(points, shrunk_points, center)