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# Decoding Transformations

In this question, each of the letters $I$, $R$, $S$ and $T$ represents a different transformation.

We can do one transformation followed by another. For example, $R S$ means ``do $R$, then $S$''.

We can also undo transformations. For example, $R^{-1}$ means ``do the inverse (opposite) of $R$''.

Here are the effects of some transformations on a shape. Can you describe the transformations $I$, $R$, $S$ and $T$?

What single transformation has the same effect as $R S T I R^{-1}S^{-1}T^{-1}I^{-1}$?

This problem is the first of three related problems.

The follow-up problems are Combining Transformations and Simplifying Transformations .

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Age 11 to 14

Challenge Level

In this question, each of the letters $I$, $R$, $S$ and $T$ represents a different transformation.

We can do one transformation followed by another. For example, $R S$ means ``do $R$, then $S$''.

We can also undo transformations. For example, $R^{-1}$ means ``do the inverse (opposite) of $R$''.

Here are the effects of some transformations on a shape. Can you describe the transformations $I$, $R$, $S$ and $T$?

What single transformation has the same effect as $R S T I R^{-1}S^{-1}T^{-1}I^{-1}$?

This problem is the first of three related problems.

The follow-up problems are Combining Transformations and Simplifying Transformations .

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?