Hi, the complete original question is:

f and g are both affine transformations. The transformation f is a reflection in the line x=2, and the transformation g maps the points (0,0), (1,0) and (0,1) to the points (0, -4), (0, -3) and (-1, -4) respectively.

a) determine g (in the form g(x) Ax + a, where A is a 2x2 matrix and a is a vector with two components.

b) Exprerss f as a composite of three transformations: a translation, followed by a reflection in a line through the origin, followed by a translation. Hence determine f (in the same form as you found g in part a)).

c) Fine the affine transformation g o f (in the same form as you found g in part a)).

d) Given that g o f is either a rotation or a reflection, state which it is. If it is a rotation, state the centre and angle of rotation. If it is a reflection, state the axis of reflection. Justify your answer.

For a) I found that (g = Bx + b) g(x) =

$\displaystyle \left(\begin{array}{cc}0&-1\\1&0\end{array}\right)$ + $\displaystyle \left(\begin{array}{cc}0\\-4\end{array}\right)$

For b) I found that (f = Ax + a) f(x) =

$\displaystyle \left(\begin{array}{cc}-1&0\\0&1\end{array}\right)$ + $\displaystyle \left(\begin{array}{cc}4\\0\end{array}\right)$

c) I am unsure how to combine the two answers above. I thought something like: (?)

g o f = g(f(x))

= g(Ax + a)

= B(Ax + a) + b

d) Also I am not sure how to work out this question.

Any help would be much appreciated. Thanks for your help in advance.

Kind regards,

Cozza