Coordinate Pairs with ZerosDate: 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/ |
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