SO, here is the problem:
A reflection in the line y = x - 1 is followed by an anticlockwise rotation of about the point (-1,1). Show that the resultant transformation has an invariant line, and give the equation of this line. Describe the resultant transformation in relation to this line.
For the first transformation I get :
For the second the rotation about the origin O is:
and about (-1,1) is:
The resultant of a process P that transforms x to x' (i.e. x' = Px) and is followed by a process Q that transforms x' to x'' (i.e. x'' = Qx') is the resultant process x'' = QPx. So:
The result of this transformation on the unit square OABC is as follows:
O(0,0) goes to O(0,2)
I have attached a rough sketch. It is not what I was hoping for. The answer is that the transform is a glide reflection in the line x = 1/2 with ((1/2,0) going to (1/2, 3). My transformation doesn't even preserve a closed shape. If you ignore the sequence of the letters OABC it looks like a shear along x = 1/2. Can anyone see what I am doing wrong?