Square Pair
Why do this problem?
This problem builds students' understanding of matrix transformations in two dimensions and encourages exploration which will increase confidence at working with vectors and matrices. Insight gained from geometrical approaches leads to a better understanding of matrix algebra.
Possible approach
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.
Key questions
What can you say about the image of the points on a line after transformation by a matrix?
Possible extension
Transformations for 10 offers a variety of challenging questions about the effects of matrices in two and three dimensions, with an emphasis on thinking geometrically.
Possible support
Begin with lots of examples of transforming the points $(0,0), (0,1), (1,0), (1,1)$ by multiplying by different matrices. Plot the resulting four points each time, and share ideas about what is common to all the images.
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