Translations

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

The white square slides once around the pink square. Through what distance does the point P on the white square move?

Make a footprint pattern using only reflections.

Does changing the order of transformations always/sometimes/never produce the same transformation?

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

Weekly Problem 2 - 2009
The 16 by 9 rectangle is cut as shown. Rearrange the pieces to form a square. What is the perimeter of the square?

Points off a rolling wheel make traces. What makes those traces have symmetry?

Can you swap the black knights with the white knights in the minimum number of moves?