Loci in the Argand Plane Geogebra

To use this tool without downloading anything, click here.

I wrote a detailed description of how I use this in a lesson on my blog.

In brief:

There is a slider which chooses the type of locus you want to focus on.

Type 1: | z - a | = r
You can control the position of the points representing a and z.

Type 2: | z - a | = | z - b |
You can control the positions of the points representinga, b and z.

Type 3: Arg(z-a) = alpha
You can control the positions of a and z.

You can use the page to test whether points on the plane satisfy a given equation or inequality. You can join the dots to find the right shapes:

Type 1: | z - a | = r A circle of radius r centred at (Re(a),Im(a))

Type 2: | z - a | = | z - b | The perpendicular bisector of (Re(a),Im(a)) and (Re(b),Im(a))

Type 3: Arg(z-a) = alpha The half-line which is alpha radians anticlockwise from the Real-axis direction beginning at (Re(a),Im(a))

I hope this is useful for you.

Please feel free to comment on my blog if you have suggestions for improving the tool.

Do you have any ideas for memorising these different types of locus? Like an acronym or a mnemonic?

If you find it useful, please write a review on TES.com.

Thanks!