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Answers
dinate and the second value is the y-coordinate. Note that the x-coordinate is listed before the y-coordinate. Since the origin has an x-coordinate of 0 and a y-coordinate of 0, its ordered pair is written (0, 0).
Consider the point below.
To identify the location of this point, start at the origin (0, 0) and move right along the x-axis until you are under the point. Look at the label on the x-axis. The 4 indicates that, from the origin, you have traveled four units to the right along the x-axis. This is the x-coordinate, the first number in the ordered pair.
From 4 on the x-axis move up to the point and notice the number with which it aligns on the y-axis. The 3 indicates that, after leaving the x-axis, you traveled 3 units up in the vertical direction, the direction of the y-axis. This number is the y-coordinate, the second number in the ordered pair. With an x-coordinate of 4 and a y-coordinate of 3, you have the ordered pair (4, 3).
Let’s look at another example.
Example
Problem
Describe the point shown as an ordered pair.
(5, y)
Begin at the origin and move along the x-axis. This is the x-coordinate and is written first in the ordered pair.
(5, 2)
Move from 5 up to the ordered pair and read the number on the y-axis. This is the y-coordinate and is written second in the ordered pair.
Answer
The point shown as an ordered pair is (5, 2).
Plotting Points in the Coordinate Plane
Now that you know how to use the x- and y-axes, you can plot an ordered pair as well. Just remember, both processes start at the origin—the beginning! The example that follows shows how to graph the ordered pair (1, 3).
Example
Problem
Plot the point (1, 3).
The x-coordinate is 1 because it comes first in the ordered pair. Start at the origin and move a distance of 1 unit in a positive direction (to the right) from the origin along the x-axis.
The y-coordinate is 3 because it comes second in the ordered pair. From here move directly 3 units in a positive direction (up). If you look over to the y-axis, you should be lined up with 3 on that axis.
Answer
Draw a point at this location and label the point (1, 3).
In the previous example, both the x- and y-coordinates were positive. When one (or both) of the coordinates of an ordered pair is negative, you will need to move in the negative direction along one or both axes. Consider the example below in which both coordinates are negative.
Example
Problem
Plot the point (−4, −2).
The x-coordinate is −4 because it comes first in the ordered pair. Start at the origin and move 4 units in a negative direction (left) along the x-axis.
The y-coordinate is −2 because it comes second in the ordered pair. Now move 2 units in a negative direction (down). If you look over to the y-axis, you should be lined up with −2 on that axis.
Answer
Draw a point at this location and label the point (−4, −2).
The steps for plotting a point are summarized below.
Steps for Plotting an Ordered Pair (x, y) in the Coordinate Plane
o Determine the x-coordinate. Beginning at the origin, move horizontally, the direction of the x-axis, the distance given by the x-coordinate. If the x-coordinate is positive, move to the right; if the x-coordinate is negative, move to the left.
o Determine the y-coordinate. Beginning at the x-coordinate, move vertically, the direction of the y-axis, the distance given by the y-coordinate. If the y-coordinate is positive, move up; if the y-coordinate is negative, move down.
o Draw a point at the ending location. Label the point with the ordered pair.
Which point represents the ordered pair (−2, −3)?
Show/Hide Answer
The Four Quadrants
Ordered pairs within any particular quadrant share certain characteristics. Look at each quadrant in the graph below. What do you notice about the signs of the x- and y-coordinates of the points within each quadrant?
Within each quadrant, the signs of the x-coordinates and y-coordinates of each ordered pair are the same. They also follow a pattern, which is outlined in the table below.
Quadrant
General Form of Point in this Quadrant
Example
Description
I
(+, +)
(5, 4)
Starting from the origin, go along the x-axis in a positive direction (right) and along the y-axis in a positive direction (up).
II
(−, +)
(−5, 4)
Starting from the origin, go along the x-axis in a negative direction (left) and along the y-axis in a positive direction (up).
III
(−, −)
(−5, −4)
Starting from the origin, go along the x-axis in a negative direction (left) and along the y-axis in a negative direction (down).
IV
(+, −)
(5, −4)
Starting from the origin, go along the x-axis in a positive direction (right) and along the y-axis in a negative direction (down).
Once you know about the quadrants in the coordinate plane, you can determine the quadrant of an ordered pair without even graphing it by looking at the chart above. Here’s another way to think about it.