Reflections

Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only one centre of rotation ? Or if you thought that was impossible, could you say why ?

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?

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?

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

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