Learning Outcomes
- Identify points on a graph
In algebra, being able to identify the coordinates of a point shown on a graph is just as important as being able to plot points. To identify the x-coordinate of a point on a graph, read the number on the x-axis directly above or below the point. To identify the y-coordinate of a point, read the number on the y-axis directly to the left or right of the point. Remember, to write the ordered pair using the correct order [latex]\left(x,y\right)[/latex].
Consider the point below.
To identify the location of this point, start at the origin [latex](0, 0)[/latex] and move right along the x-axis until you are under the point. Look at the label on the x-axis. The [latex]4[/latex] 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 [latex]4[/latex] on the x-axis move up to the point and notice the number with which it aligns on the y-axis. The [latex]3[/latex] indicates that, after leaving the x-axis, you traveled [latex]3[/latex] 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 [latex]4[/latex] and a y-coordinate of [latex]3[/latex], you have the ordered pair [latex](4, 3)[/latex].
Let’s look at another example.
Example
Describe the point shown as an ordered pair.
Describe the point shown as an ordered pair
example
Name the ordered pair of each point shown:
Solution
Point A is above [latex]-3[/latex] on the [latex]x\text{-axis}[/latex], so the [latex]x\text{-coordinate}[/latex] of the point is [latex]-3[/latex]. The point is to the left of [latex]3[/latex] on the [latex]y\text{-axis}[/latex], so the [latex]y\text{-coordinate}[/latex] of the point is [latex]3[/latex]. The coordinates of the point are [latex]\left(-3,3\right)[/latex].
Point B is below [latex]-1[/latex] on the [latex]x\text{-axis}[/latex], so the [latex]x\text{-coordinate}[/latex] of the point is [latex]-1[/latex]. The point is to the left of [latex]-3[/latex] on the [latex]y\text{-axis}[/latex], so the [latex]y\text{-coordinate}[/latex] of the point is [latex]-3[/latex]. The coordinates of the point are [latex]\left(-1,-3\right)[/latex].
Point C is above [latex]2[/latex] on the [latex]x\text{-axis}[/latex], so the [latex]x\text{-coordinate}[/latex] of the point is [latex]2[/latex]. The point is to the right of [latex]4[/latex] on the [latex]y\text{-axis}[/latex], so the [latex]y\text{-coordinate}[/latex] of the point is [latex]4[/latex]. The coordinates of the point are [latex]\left(2,4\right)[/latex].
Point D is below [latex]4[/latex] on the [latex]x-\text{axis}[/latex], so the [latex]x\text{-coordinate}[/latex] of the point is [latex]4[/latex]. The point is to the right of [latex]-4[/latex] on the [latex]y\text{-axis}[/latex], so the [latex]y\text{-coordinate}[/latex] of the point is [latex]-4[/latex]. The coordinates of the point are [latex]\left(4,-4\right)[/latex].
try it
example
Name the ordered pair of each point shown:
try it
Watch the following video for another example of how to determine the ordered pair for points on the coordinate plane.
