Plot Ordered Pairs

Learning Objectives

  • Plot Ordered Pairs
    • Identify the components of the coordinate plane
    • Plot ordered pairs on the coordinate plane

The Components of the Coordinate Plane

You have likely used a coordinate plane before. For example, have you ever used a gridded overlay to map the position of an object? (This is often done with road maps, too.)

A picture of a manhole that says Drain and a small blue object. The picture has a grid overlaying it, with the columns labeled at the top A through F. On the left, each row is labeled with 1 through 6. The small blue object is in square 4F.

This “map” uses a horizontal and vertical grid to convey information about an object’s location. Notice that the letters A–F are listed along the top, and the numbers 1–6 are listed along the left edge. The general location of any item on this map can be found by using the letter and number of its grid square. For example, you can find the item that exists at square “4F” by moving your finger along the horizontal to letter F and then straight down so you are in line with the 4. You’ll find a blue disc is at this location on the map.

The coordinate plane has similar elements to the grid shown above. It consists of a horizontal axis and a vertical axis, number lines that intersect at right angles. (They are perpendicular to each other.)

A graph with an x-axis running horizontally and a y-axis running vertically. The location where these axes cross is labeled the origin, and is the point zero, zero. The axes also divide the graph into four equal quadrants. The top right area is quadrant one. The top left area is quadrant two. The bottom left area is quadrant three. The bottom right area is quadrant four.

The horizontal axis in the coordinate plane is called the x-axis. The vertical axis is called the y-axis. The point at which the two axes intersect is called the origin. The origin is at 0 on the x-axis and 0 on the y-axis.

Locations on the coordinate plane are described as ordered pairs. An ordered pair tells you the location of a point by relating the point’s location along the x-axis (the first value of the ordered pair) and along the y-axis (the second value of the ordered pair).

In an ordered pair, such as (x, y), the first value is called the x-coordinate 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.

Grid with x-axis and y-axis. A blue dotted line extends from the origin, which is the point (0,0) along the horizontal x-axis to 4. A red dotted line goes up vertically from 4 on the x-axis to 3 on the y-axis. That point is labeled (4, 3).

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

Describe the point shown as an ordered pair.

A point that is 2 spaces above the x-axis and 5 spaces to the right of the y-axis.

Describe the point shown as an ordered pair

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

Plot 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

Plot the point [latex](−4,−2)[/latex].

Graph with blue arrow pointing from origin to four units to the left. A red arrow points down 2 spaces to the point negative 4, negative 2.

The x-coordinate is [latex]−4[/latex] 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 [latex]−2[/latex] 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 [latex]−2[/latex] on that axis.

The steps for plotting a point are summarized below.

Steps for Plotting an Ordered Pair (x, y) in the Coordinate Plane

  • 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.
  • 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.
  • Draw a point at the ending location. Label the point with the ordered pair.

Here are some more examples with plotting points on the coordinate plane.