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This topic is part of the TCS FREE high school mathematics 'How-to Library', and will help you to use the distance formula to find distances between (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:

The distance 'd' between the points A = (x1, y1) and B = (x2, y2) is given by the formula:

This formula is an application of Pythagoras' theorem for right triangles:

For example, consider the two points A (1,4) and B (4,0),

so:  x₁ = 1,  y₁ = 4,  x₂ = 4, and y₂ = 0.

Substituting into the distance formula we have:

Method:

Maths Helper Plus can use the distance formula to find the distance between two points. Also, it will show you the working steps and draw a labelled diagram.  

 

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:

x₁ = A,  y₁ = D,  x₂ = B, and y₂ = X.

To calculate the distance between any two points, enter the coordinates into the edit boxes.

 

To enter the coordinates, click on the 'A' edit box with the mouse, then type the x₁ coordinate. Now click on the 'D' edit box and type the y₁ 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.