Rotations

Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.

How many different transformations can you find made up from combinations of R, S and their inverses? Can you be sure that you have found them all?

What groups of transformations map a regular pentagon to itself?

Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?

What happens to these capital letters when they are rotated through one half turn, or flipped sideways and from top to bottom?

Find the shape and symmetries of the two pieces of this cut cube.

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?