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## 'Surprising Transformations' printed from http://nrich.maths.org/

This problem follows on from

Translating
Lines and

Reflecting
Lines.
I took the graph $y=4x+7$ and performed the four transformations
shown on the cards below.

Unfortunately, I can't remember the order in which I carried
out the four transformations, but I know that I ended up with the
graph of $y=4x-2$.

Find an order in which I could have carried out the
transformations.

There is more than one way of doing this - can you find them
all?

Try to explain why different orders can lead to the same
outcome.

What other lines could I have ended up with if I had performed
the four transformations in a different order?