Midpoint formula
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How to use the midpoint formula to find the midpoint of a line between two (x,y) points.

This topic is part of the TCS FREE high school mathematics 'How-to Library', and will help you to use the midpoint formula to find the midpoint of a line between two (x,y) points.
(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.

Theory:

A(xa,ya) and B(xb,yb) are two points in the (x,y) plane, and P(xp,yp) is the midpoint of the line joining A and B:


The coordinates of the midpoint P are given by:

                             and    

For example, find the midpoint of the line joining the points A(-4,-3) and B(4,5).

Substituting into the formulas we have:

and

So the midpoint of AB is: P(0,1)

 

Method:

Maths Helper Plus can use the midpoint formula to find the midpoint 'P' between two given points 'A' and 'B'. Also, it will show you the working steps and draw a labelled diagram.  

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

File name:  'Midpoint Formula.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:

 

The coordinates of the two (x,y) points are entered into the four edit boxes 'A', 'B', 'C' and 'D', as follows:

xa = A,  ya = D,  xb = B, and yb = X.

To calculate the coordinates of the midpoint between points 'A' and 'B', enter the coordinates into the edit boxes.

 

To enter the coordinates, click on the 'A' edit box with the mouse, then type the xa coordinate. Now click on the 'D' edit box and type the ya coordinate. Continue until the four coordinates are entered, then click the 'Update' button.

 

Step 3  Adjust the scale of the labelled diagram

If the labelled diagram does not display the points, the scale needs to be reduced. In this case, briefly press the F10 key enough times until the two plotted points are seen.

 

You can make the diagram bigger by holding down 'Ctrl' while you press F10.

 

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