There are several “rigid transformations” in dynamic geometry, which move an object around without changing its size or shape. See the tool menu for GeoGebra transformation tools.
* Translate by Vector -- creates a copy of the object at a distance and in a direction determined by a “vector” (a segment pointing in a direction).
* Reflect about Line -- creates a copy of the object flipped across a line.
* Rotate around Point -- creates a copy of the object rotated around a point.
In GeoGebra, a transformation of a figure like triangle ABC creates a congruent figure that is dependent on the original figure. In a translation, the new figure is moved or displaced in the distance and direction indicated by a vector. A vector is like a segment except that it has a particular direction as well as a length.
In this activity, triangle ABC is translated to triangle XYZ. To do this, point A is translated to point X by the distance and direction of vector DE.
Construct your own figure and vector. Translate your figure a couple of times and do a drag test to see if the figures stay congruent and what difference different vectors make.