The Cartesian Coordinate System
The Cartesian coordinate system consists of two real number lines
placed at right angles to each other.
The horizontal number line is called the xaxis.
The vertical number line is called the yaxis.
The axes define a flat surface called the xyplane.
Every point in the xyplane has two numbers associated with it.
â€¢ The xcoordinate or abscissa tells how far the point lies to the left or
right of the yaxis.
â€¢ The ycoordinate or ordinate tells how far the point lies above or below
the xaxis.
The xcoordinate and the ycoordinate are often written inside parentheses,
like this: (x, y).
The first number, x, represents the xcoordinate and the second number,
y, represents the ycoordinate.
For example, the point that is 3 units to the right of the yaxis and 6 units
below the xaxis is labeled (3, 6).Because the order in which the pair of numbers is written is important,
(x, y) is called an ordered pair. Thus, the point (6, 3) is not the same as
the point (3, 6).
The xaxis and the yaxis intersect at the point (0, 0). This point is called
the origin.
The xaxis and the yaxis divide the xyplane into four regions called quadrants.
Quadrant
I
II
III
IV 
Sign of x
positive
negative
negative
positive 
Sign of y
positive
positive
negative
negative 
A point on an axis does not lie in a quadrant.
Example 1Find the coordinates of each point
labeled on the graph.
Then, state the quadrant in which
each point lies.
Solution
Point A has coordinates (2, 5), and lies in Quadrant I.
Point B has coordinates (3, 4), and lies in Quadrant IV.
Point C has coordinates (5, 3), and lies in Quadrant II.
Point D has coordinates (6, 2), and lies in Quadrant III.
Point E has coordinates (5, 0). It is not in a quadrant since it lies on the
xaxis.
Example 2
Plot each point on a Cartesian coordinate system:
a. (5, 4)
b. (4, 6)
c. (3, 0)
d. (0, 3)
Solution
The plot the point (5, 4), start at the origin:
â€¢ move 5 units to the right;
â€¢ then move down 4 units;
â€¢ place a dot at this location.
Follow a similar procedure for the other points. Notice the difference
between the locations of points (3, 0) and (0, 3).
