#
Section 2-1

#
Graphing Ordered Pairs

A
Cartesian plane
(named after French mathematician Rene Descartes, who formalized
its use in mathematics) is defined by two perpendicular number lines: the
**
***
x
*
-axis
,
which is horizontal, and the
**
***
y
*
-axis
, which is vertical.
Using these axes, we can describe any point in the plane using an
ordered
pair
of numbers.

The Cartesian plane extends infinitely in all directions. To show this, math
textbooks usually put arrows at the ends of the axes in their drawings.

The coordinates of a point in the plane are measured in relation to a "central" point,
the origin : first to the right, then up. The coordinates are listed as (
*
x
*
,
*
y
*
)
for (over, up). (Negative numbers are used for left and down.) In the picture,
the origin is the blue dot. Three other points and their corresponding ordered
pairs are shown.

The Cartesian plane is divided into four quadrants . These are numbered from
I - IV, starting with the upper right and going around counterclockwise. (For
some reason everybody uses roman numerals for this).

In Quadrant I, both the
*
x
*
- and
*
y
*
-coordinates are positive;
in Quadrant II, the
*
x
*
-coordinate is negative, but the
*
y
*
-coordinate
is positive; in Quadrant III both are negative; and in Quadrant IV
*
x
*
is
positive but
*
y
*
is negative.

Points which lie on an axis (i.e., which have at least one coordinate equal
to 0) are said not to be in any quadrant.