There were no solutions sent in to this problem
so it becomes a Tough Nut.
<br />
<br />However it looks
longer and more complicated than it really is
because you have been given lots of information
in the question to lead you by fairly small and 
obvious steps to the solution and the diagram
should help you see why you get a reflection in
the line 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>y</mi><mo>=</mo><mi>x</mi><mi>tan</mi><mi>&#x03B8;</mi></mrow></math>.
<br />
<br />You need to understand
how a matrix represents a transformation of the
plane and how it operates on each point to give
its image under that transformation. See the
problem 'The Matrix' from July 2003 and its
solution 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.
<br />
<br />
Have a go, this is not so difficult.

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