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## 'Mirror, Mirror...' printed from http://nrich.maths.org/

You might like to copy the diagram above onto

squared paper to help you with this
problem.

Reflect the flag in the left-hand line, and then reflect the image
you obtain in the right-hand line. Can you describe the single
transformation that takes the first flag to the last flag?

Repeat this with flags in different positions and orientations, and
with different pairs of parallel lines.

Does it matter in which line you reflect first?

Does it matter whether the flag is to one side of the lines or
between the lines?

Try to find a way to describe the single transformation for a
general pair of parallel lines.

Can you prove your answer?

If you have enjoyed this problem, why not have a go at

...on the Wall and

Who is the fairest of them all? ?