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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?

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.

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.