Coordinate Pairs with Zeros

Date: 03/15/2004 at 12:04:03
From: Mark
Subject: Coordinates containting zero are in what quadrant?

If a coordinate pair contains a zero, which quadrant is it in?  For
example, is the point (2,0) in the 1st or 4th quadrant?

Date: 03/15/2004 at 16:16:41
From: Doctor Douglas
Subject: Re: Coordinates containting zero are in what quadrant?

Hi Mark.

Thanks for writing to the Math Forum.  Most mathematics dictionaries
that I have seen define the quadrant only for both x and y nonzero:

  quadrant I:  x > 0, y > 0
  quadrant II:  x < 0, y > 0
  quadrant III:  x < 0, y < 0
  quadrant IV:  x > 0, y < 0

See for example, 

  Eric W. Weisstein's Mathworld
    http://mathworld.wolfram.com/Quadrant.html 

So, the standard and accepted answer to your question is that points
with zeros, which will fall on the axes, are not considered to be in
any quadrant.

Now, if you want, it is possible to define things so that a point with 
a single zero coordinate either

  (1) is common to the two adjacent quadrants, or
  (2) is part of one and only one quadrant.

A natural way to accomplish defintion (2) above is to associate the 
positive x-axis with quadrant I, the positive y-axis with quadrant II, 
the negative x-axis with quadrant III, and the negative y-axis with 
quadrant IV.  But even then, it would not be particularly elegant to 
decide to which quadrant one should assign the "extra" point at the
origin (0,0).

The best answer for standard high school math?  Points on the axes are
not in a quadrant--they lie on the quadrant boundaries.  

- Doctor Douglas, The Math Forum
  http://mathforum.org/dr.math/