I am going through this past papers and I am utterly confused with the question- looked at all the notes and examples but simply can't understand what to do for part (b) Please explain. I have sucessfully done part (a) and answer is:

A= (-2 - -2, -1+2

3-2 2-2) = (0 1

1 0)

And a = (-2

2)

Hence g(x) = (0 1 + (-2

1 0)x 2)

this is the whole question:

In this question, f and g are both affine transformations. The

transformation f is reflection in the line y = 1, and the transformation g

maps the points (0, 0), (1, 0) and (0, 1) to the points (−2, 2), (−2, 3) and

(−1, 2), respectively.

(a) Determine g (in the form g(x) = Ax + a, where A is a 2×2 matrix

and a is a vector with two components).

(b) Express f as a composite of three transformations: a translation,

followed by 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) Use the expressions that you found for f and g in parts (a) and (b) to

calculate f(g(x)), and hence find the affine transformation f ◦ g in the

same form as you found g in part (a).

Thank you