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?
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.
Investigate the transfomations of the plane given by the 2 by 2
matrices with entries taking all combinations of values 0. -1 and
+1.
Rots and Refs
Age 16 to 18 Challenge Level
See the problem
'The Matrix' for an explanation of how a transformation of the
plane is given by a matrix and how you can find the image of a
point by multiplying its vector by the matrix of the
transformation.