(self, parameter='t')
return Point(x, y)
A parameterized point on the Line.

        Parameters
        ==========

        parameter : str, optional
            The name of the parameter which will be used for the parametric
            point. The default value is 't'. When this parameter is 0, the
            first point used to define the line will be returned, and when
            it is 1 the second point will be returned.

        Returns
        =======

        point : Point

        Raises
        ======

        ValueError
            When ``parameter`` already appears in the Line's definition.

        See Also
        ========

        sympy.geometry.point.Point

        Examples
        ========

        >>> from sympy import Point, Line
        >>> p1, p2 = Point(1, 0), Point(5, 3)
        >>> l1 = Line(p1, p2)
        >>> l1.arbitrary_point()
        Point(4*t + 1, 3*t)
A parameterized point on the Line.
A parameterized point on the Line .
def arbitrary_point(self, parameter='t'):
        """A parameterized point on the Line.

        Parameters
        ==========

        parameter : str, optional
            The name of the parameter which will be used for the parametric
            point. The default value is 't'. When this parameter is 0, the
            first point used to define the line will be returned, and when
            it is 1 the second point will be returned.

        Returns
        =======

        point : Point

        Raises
        ======

        ValueError
            When ``parameter`` already appears in the Line's definition.

        See Also
        ========

        sympy.geometry.point.Point

        Examples
        ========

        >>> from sympy import Point, Line
        >>> p1, p2 = Point(1, 0), Point(5, 3)
        >>> l1 = Line(p1, p2)
        >>> l1.arbitrary_point()
        Point(4*t + 1, 3*t)

        """
        t = _symbol(parameter)
        if t.name in (f.name for f in self.free_symbols):
            raise ValueError('Symbol %s already appears in object '
            'and cannot be used as a parameter.' % t.name)
        x = simplify(self.p1.x + t*(self.p2.x - self.p1.x))
        y = simplify(self.p1.y + t*(self.p2.y - self.p1.y))
        return Point(x, y)
def arbitrary_point ( self , parameter = 't' ) : t = _symbol ( parameter ) if t . name in ( f . name for f in self . free_symbols ) : raise ValueError ( 'Symbol %s already appears in object ' 'and cannot be used as a parameter.' % t . name ) x = simplify ( self . p1 . x + t * ( self . p2 . x - self . p1 . x ) ) y = simplify ( self . p1 . y + t * ( self . p2 . y - self . p1 . y ) ) return Point ( x , y )