How to use the LocusEquation command?

Zoltán Kovács, May 29, 2014

This book is an introduction to the LocusEquation command in GeoGebra, available since version 4.2. Its target audience is teachers who work in secondary schools. To compute locus equations, efficient algorithms may be required. Since version 4.4 such equations can be quickly displayed not only in desktop mode in GeoGebra, but also in a web browser (even on tablets). There are, however, some tricks which are important to know. This step-by-step howto helps in technical questions primarily, but the demo applets can be further developed to be full featured student applets as well.


  • 1. Linear locus equation
  • 2. Quadratic locus equation
  • 3. Quadratic locus equation with dynamic coordinates
  • 4. Discovering the Simson-Wallace theorem
  • 5. Holfeld's 35th problem as an implicit locus

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Linear locus equation

This applet demonstrates the basics of creating a locus equation object in GeoGebra.

[list=1] [*]In Step 1 line AB (denoted by "a") is defined. [*]In Step 2 its equation is also displayed (numerically). [*]Now we define point C and mirror the line to the point (Step 3). How? In Step 4 we put point D on line a and mirror it on C (Step 5) to get point D'. [*]Now the locus of point D' while point D is moving on line a, is the mirror image of line a, i.e. the mirrored line a' (Step 6). [*]Finally in Step 7 we obtain the equation of line a'. [/list] Some actions to try out: [list=1] [*]Drag point D and check that D' is its mirror image to point C. [*]Drag point C and try to search for such a place for it to make the coefficients of equation a' to be "larger" numbers. Note that these coefficients are always integers. [*]Drag points A and B as well. Note that the equation of line a may contain numeric values, i.e. it is computed numerically. [/list] Dragging may be slow under some systems and conditions. Turn on the next page to learn how to speed up animation in such cases.
– Zoltán Kovács

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