26 January 2021

Last year I spent a couple of wonderful days in Madrid, right before the first lockdown of the COVID-19 pandemic. I visited my friends in Spain in the frame of an ERASMUS project. I also managed to meet Eugenio-Roanes Lozano, full professor of mathematics at the Department of Mathematics Education at Complutense University (or, more precisely at Depto. de Didactica de las Ciencias Experimentales, Sociales y Matematicas, Facultad de Educacion, Universidad Complutense de Madrid). Eugenio had an idea to extend GeoGebra with the following feature.

Given a planar construction with a couple of transformations, including reflections, rotations, translations or scaling. For example, for a given point \(P\) a reflection about a line \(\ell\) defines the point \(P'\). Now, given another point \(Q\) we may want to copy this transformation and obtain the point \(Q'\) automatically.

By entering the command Q'=ApplyMap({P,P'},Q) we can obtain the sought point \(Q'\). (Just copy-paste the command into the applet to give it a try.)

Note: This feature is in a prototype state. That is, it works only for reflections at the moment and it does not work reliably. Expect problems when using it.

See also the ApplyMatrix command (it already exists in GeoGebra for a long time).