See the effects of some combined transformations on a shape. Can you describe what the individual transformations do?

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

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?

In the diagram the radius length is 10 units, OP is 8 units and OQ is 6 units. If the distance PQ is 5 units what is the distance P'Q' ?

In the diagram the point P' can move to different places along the dotted line. Each position P' takes will fix a corresponding position for P. If P' moves along a straight line what does P do ?

In the diagram the point P can move to different places around the dotted circle. Each position P takes will fix a corresponding position for P'. As P moves around on that circle what will P' do?

Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?

There are an infinite number of ways in which Mr McGregor can ensure that all his gardens have the same number of plants.

An introduction to groups using transformations, following on from the October 2006 Stage 3 problems.