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.

Reflect Again

Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.

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.

Square Pair

Stage: 5 Challenge Level:
Try transforming the points of $S$ using some different $2 \times 2$ matrices and record the resulting points on a grid. What do you notice?

This problem uses mathematical ideas met in Further Pure Mathematics A Level modules.