Is it possible for a point plotted in the cartesian coordinate system to not lie in one of the four quadrants?

The answer is yes.
 In a 2D coordinate system, any point P (xo, yo) that is plotted in the plane must be contained in one of the four quadrants. However, there are points that are only contained in one of the axes of the Cartesian plane.
 Example: the point (0,1)
 answer
 Yes, it is possible.