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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 (x,y)\left(x,y\right). 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)(0, 0) and move right along the x-axis until you are under the point. Look at the label on the x-axis. The 44 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 44 on the x-axis move up to the point and notice the number with which it aligns on the y-axis. The 33 indicates that, after leaving the x-axis, you traveled 33 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 44 and a y-coordinate of 33, you have the ordered pair (4,3)(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.

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>)(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)(5,2)

Answer

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

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 3-3 on the x-axisx\text{-axis}, so the x-coordinatex\text{-coordinate} of the point is 3-3. The point is to the left of 33 on the y-axisy\text{-axis}, so the y-coordinatey\text{-coordinate} of the point is 33. The coordinates of the point are (3,3)\left(-3,3\right). Point B is below 1-1 on the x-axisx\text{-axis}, so the x-coordinatex\text{-coordinate} of the point is 1-1. The point is to the left of 3-3 on the y-axisy\text{-axis}, so the y-coordinatey\text{-coordinate} of the point is 3-3. The coordinates of the point are (1,3)\left(-1,-3\right). Point C is above 22 on the x-axisx\text{-axis}, so the x-coordinatex\text{-coordinate} of the point is 22. The point is to the right of 44 on the y-axisy\text{-axis}, so the y-coordinatey\text{-coordinate} of the point is 44. The coordinates of the point are (2,4)\left(2,4\right). Point D is below 44 on the xaxisx-\text{axis}, so the x-coordinatex\text{-coordinate} of the point is 44. The point is to the right of 4-4 on the y-axisy\text{-axis}, so the y-coordinatey\text{-coordinate} of the point is 4-4. The coordinates of the point are (4,4)\left(4,-4\right).
 

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