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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def points_are_in_a_straight_line( points, tolerance=1e-7 ):
 """ Check whether a set of points fall on a straight line. Calculates the areas of triangles formed by triplets of the points. Returns False is any of these areas are larger than the tolerance. Args: points (list(np.array)):
 list of Cartesian coordinates for each point. tolerance (optional:float):
 the maximum triangle size for these points to be considered colinear. Default is 1e-7. Returns: (bool):
 True if all points fall on a straight line (within the allowed tolerance). """

    a = points[0]
    b = points[1]
    for c in points[2:]:
        if area_of_a_triangle_in_cartesian_space( a, b, c ) > tolerance:
            return False
    return True