This GeoGebra activity is designed as an introduction of translations, rotations, and reflections.
1. Given Polygon F, use slider α or the Rotate button to rotate the polygon α°. Notice the
length of segment BB’. Notice the length of segment AJ and A’J’.
a. At what angle(s) of rotation will length AJ not equal A’J’?
b. At what angle(s) of rotation will point A’ be completely below point A?
c. At what angle(s) of rotation will Polygon F’ completely cover Polygon F?
d. At what angle of rotation will point k be the midpoint of BB’?
e. What is the center of rotation?
2. Given Polygon T, use the ‘Translate T’ button to translate Polygon T by Vector u.
a. Based on the vector u, describe the transformation.
b. What has changed about the length of each segment?
c. What are the original coordinates of each point of polygon T?
d. What are the new coordinates of each point of Polygon T?
e. Can you find the length of u?
3. Given Polygon R, use the ‘Translate R’ button to translate Polygon R by Vector v.
a. What has changed about the length of each segment?
b. What are the original coordinates of each point of polygon R?
This GeoGebra activity is designed as an introduction of translations, rotations, and reflections.
c. What are the new coordinates of each point of Polygon R?
d. Can you find the length of v?
e. Make a conjecture about Translations of polygons:
4. Given Polygons S and T, use the respective Reflect buttons to reflect each polygon about
the given line.
To start this exercise, set m = 0 and b = -1.
a. What has changed about the length of each segment?
b. What are the original coordinates of each point of polygon S? Polygon T?
c. What are the new coordinates of each point of polygon S? Polygon T?
5. Now choose your own values for m and b.