Hi folks,

Given the following transformation:

$\displaystyle \overline{x'} =

\left( \begin{array}{cc} -2 & 0 \\ 0 & 2 \end{array} \right)

\left( \begin{array}{c} x \\ y \end{array} \right) +

\left( \begin{array}{c} 4 \\ 0 \end{array} \right)$

show that it may be expressed as a reflection in the line x = 4/3 followed by an enlargement and give the centre and scale factor of this enlargement.

using:

$\displaystyle x' = -2x + 4 $

$\displaystyle y' = 2y$

I have plotted the results of the transformation as shown in the diagram. As far as I can see, the transform represents a reflection about x = 1 and an enlargement, scale factor 2 about the origin. The first part of my diagram shows the transformation, the second the reflection about x = 1 and the third the enlargement. Just to clarify this last bit: If the enlargement had a cenre at A (1,0) then A would stay where it is, O would move to (3,0) B would go to (3,2) and C to (1,2) but if we move the centre back to the origin, we should get the result in the top part of the diagram.

I just don't see any way that the transform can be a reflection in x = 4/3 floowed by an enlargement of 2 centre (4/3, 0) which is the answer provided!

Can anyone help? It's not so hard, is it?