# Identifying Points on a Rectangular Coordinate System

### Learning Outcomes

- Identify points on a graph

*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.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: 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: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]## Contribute!

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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.

### CC licensed content, Specific attribution

- Prealgebra.
**Provided by:**OpenStax**License:**CC BY: Attribution.**License terms:**Download for free at http://cnx.org/contents/[email protected].