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# 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 $\left(x,y\right)$. 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

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.

$(5,<i>y</i>)$

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.

$(5,2)$

The point shown as an ordered pair is $(5,2)$.

## 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 $-3$ on the $x\text{-axis}$, so the $x\text{-coordinate}$ of the point is $-3$. The point is to the left of $3$ on the $y\text{-axis}$, so the $y\text{-coordinate}$ of the point is $3$. The coordinates of the point are $\left(-3,3\right)$. Point B is below $-1$ on the $x\text{-axis}$, so the $x\text{-coordinate}$ of the point is $-1$. The point is to the left of $-3$ on the $y\text{-axis}$, so the $y\text{-coordinate}$ of the point is $-3$. The coordinates of the point are $\left(-1,-3\right)$. Point C is above $2$ on the $x\text{-axis}$, so the $x\text{-coordinate}$ of the point is $2$. The point is to the right of $4$ on the $y\text{-axis}$, so the $y\text{-coordinate}$ of the point is $4$. The coordinates of the point are $\left(2,4\right)$. Point D is below $4$ on the $x-\text{axis}$, so the $x\text{-coordinate}$ of the point is $4$. The point is to the right of $-4$ on the $y\text{-axis}$, so the $y\text{-coordinate}$ of the point is $-4$. The coordinates of the point are $\left(4,-4\right)$.

### try it

[ohm_question]146915[/ohm_question]

### example

Name the ordered pair of each point shown:

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

### 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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