Plotting ordered pairs
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How to plot ordered pairs on a graph.

This topic is part of the TCS FREE high school mathematics 'How-to Library'. It introduces the concept of an ordered pair, and shows you how to plot ordered pairs on a graph.
(See the index page for a list of all available topics in the library.) To make best use of this topic, you need to download the Maths Helper Plus software. Click here for instructions.


An 'ordered pair' is simply two numbers in a certain order. For example, the numbers '2' and '3' can form two ordered pairs:

2, 3       and      3, 2

Ordered pairs can also contain the same number twice. For example:

2, 2       and      3, 3

A very important application of ordered pairs is to locate points on a grid or map. For street maps it is common to use a letter and a number, eg: B17 or D5. This is not very accurate, but if two numbers were used instead of a number and a letter, then people would easily get them in the wrong order and get lost!

In mathematics, we use two numbers to accurately locate a position on a rectangular grid, like this:

When an ordered pair is used to locate a point on a grid, the two numbers are called the 'coordinates' of the point. In the diagram above, the point (2, 3) has been marked with a red dot. The coordinates of this point are '2' and '3'. 

On a graph grid, the point (0,0) is called the 'origin' The first coordinate of a plotted point is called the 'x' coordinate. The 'x' coordinate is the horizontal distance from the origin to the plotted point. The second coordinate of a plotted point is called the 'y' coordinate. The 'y' coordinate is the vertical distance from the origin to the plotted point.

So, to locate the point: (2, 3) on our graph grid above, we start at the origin, move 2 units horizontally and 3 units vertically.

When locating points, positive 'x' values are to the right of the origin, while negative 'x' values are to the left of the origin. Also, positive 'y' values are above the origin, while negative 'y' values are below the origin.


A. Learning about coordinates:

If you are still unsure about how to plot (x,y) points on a graph grid, or you would like to try our fun rectangular coordinate plotter, we recommend this section (part A), otherwise you can proceed to part B.

Step 1 Download the free support file... We have created a Maths Helper Plus document containing the completed example from this topic. You can use this to practice the steps described below, and as a starting point for solving your own problems.

File name:  'Coordinate plotter (rectangular).mhp'   File size: 7kb
Click here to download the file.

If you choose 'Open this file from its current location', then Maths Helper Plus should open the document immediately. If not, try the other option: 'Save this file to disk', then run Maths Helper Plus and choose the 'Open' command from the 'File' menu. Locate the saved file and open it. If you do not yet have Maths Helper Plus installed on your computer, click here for instructions.


Step 2  Display the parameters box

Press the F5 key to display the parameters box:


Click on the 'A' edit box with the mouse, then type the 'x' coordinate of your point. 

Similarly, click on the 'B' edit box and type the 'y' coordinate. 

Click the 'Update' button to refresh the diagram.

B. Plotting (x,y) coordinates:

This is how you can plot a set of (x,y) coordinates in Maths Helper Plus.

Step 1  Start with an empty Maths Helper Plus document

If you have just launched the software then you already have an empty document, otherwise hold down ‘Ctrl’ while you briefly press the ‘N’ key.


Step 2  Enter your (x,y) points

1. Press the F3 key to activate the 'input box' for typing (see below):

2. Type your own points into the input box, like this:


3. Press Enter to complete the entry


Step 3  Adjust the scale of the graph

If the graph scale is too small to display all of the points, briefly press the F10 key. This doubles the scale range in the 'x' and 'y' directions. Repeat until all plotted points are visible.


To reduce the scale again,  hold down 'Shift' while you press F10.


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