Flipping Twisty Matrices
This problem introduces the idea of how matrices can be used to represent 2D transformations. Students are then asked to consider $2 \times 2$ matrices with entries of $1$, $-1$ or $0$ and see what transformations these represent.
Students might like to use this Matrix Transformation tool to help them investigate the problem. In this tool the four corners of a quadrilateral are given as a $2 \times 4$ matrix, where the coordinates appear as the columns of the matrix, in clockwise (or anticlockwise) order. Students might like to start by changing some numbers in the matrices to see what the two matrices do.
Students can also be asked to think why the problem suggests that they consider what the matrices do to both a square and a another shape - why might considering what happens to a square not be enough?
The Matrix Transformation tool can also be used to test out students ideas as a whole class.
There are more matrix problems in this feature. The problem Square Pair follows on from this problem and considers more general 2D transformations.
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