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8 Methods for Three by One

This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different? Which do you like best?

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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.

Reflect Again

Age 16 to 18 Challenge Level:

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.