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Rots and Refs

Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.

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The Matrix

Investigate the transfomations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0. -1 and +1.

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Transformations for 10

Explore the properties of matrix transformations with these 10 stimulating questions.

Reflect Again

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The conditions suggested in the question give you two equations which you can solve to find $p'$ and $q'$. Use the same formulation to give $(p'',q'')$.

The problem 'The Matrix' explains how 2 by 2 matrices are used to give transformations of the plane and how you multiply the position vector of a point by the matrix to find the image of that point under the transformation.