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Study Guides > ALGEBRA / TRIG I

Identifying Points on a Rectangular Coordinate System

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

Answer: Begin at the origin and move along the x-axis. This is the x-coordinate and is written first in the ordered pair.

[latex](5,<i>y</i>)[/latex]

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.

[latex](5,2)[/latex]

Answer

The point shown as an ordered pair is [latex](5,2)[/latex].

Describe the point shown as an ordered pair

https://youtu.be/c9WVU34MY5Q  

example

Name the ordered pair of each point shown: The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The point 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

[ohm_question]146915[/ohm_question]
 

example

Name the ordered pair of each point shown: The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The point

Answer: Solution

Point A is on the x-axis at [latex]x=-4[/latex] The coordinates of point A are [latex]\left(-4,0\right)[/latex]
Point B is on the y-axis at [latex]y=-2[/latex] The coordinates of point B are [latex]\left(0,-2\right)[/latex]
Point C is on the x-axis at [latex]x=3[/latex] The coordinates of point C are [latex]\left(3,0\right)[/latex]
Point D is on the y-axis at [latex]y=1[/latex] The coordinates of point D are [latex]\left(0,1\right)[/latex]

 

try it

[ohm_question]146919[/ohm_question]
Watch the following video for another example of how to determine the ordered pair for points on the coordinate plane. https://youtu.be/c9WVU34MY5Q

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Licenses & Attributions

CC licensed content, Original

  • Question ID 146919, 146915, 146888, 146887, 146886, 146885, 146883. Authored by: Lumen Learning. License: CC BY: Attribution.

CC licensed content, Shared previously

  • Determine the Ordered Pairs for Points Plotted on the Coordinate Plane. Authored by: James Sousa (mathispower4u.com). License: CC BY: Attribution.

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