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Introduction to Quadrants in the Coordinate Plane

Date: 02/05/2004 at 13:36:18
From: Jon
Subject: geometry

What is a quadrant?  How do you find it?  I had to identify 9 ordered
pairs on a graph.  Now I need to also name the quadrant each one is in.



Date: 02/05/2004 at 16:22:37
From: Doctor Rob
Subject: Re: geometry

Thanks for writing to Ask Dr. Math, Jon!

In a rectangular coordinate system, the x- and y-axes divide the
plane into four regions.  These are called quadrants.  They are
numbered, often using Roman numerals:

             y
             ^
         II  |   I
             |
      <------+------>x
             |
        III  |  IV
             |

Quadrant I is also called the first quadrant, and so on.

Note that all points in each of the four quadrants share the same x
and y values in terms of positive or negative.  For example, if both
numbers are positive, the point will be in the first quadrant.  In
general:
 
  I:    x > 0, y > 0  or x positive, y positive.
  II:   x < 0, y > 0  or x negative, y positive.
  III:  x < 0, y < 0  or x negative, y negative.
  IV:   x > 0, y < 0  or x positive, y negative.

If either coordinate is 0, the point will not be in a quadrant, but
will lie on an axis.  All points with y = 0 are on the x-axis, and all
points with x = 0 are on the y-axis.  Note that the origin (0,0) is
the only point on both axes.

Feel free to write again if I can help further.

- Doctor Rob, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Coordinate Plane Geometry
High School Definitions
High School Equations, Graphs, Translations
High School Euclidean/Plane Geometry
Middle School Definitions
Middle School Graphing Equations
Middle School Two-Dimensional Geometry

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