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
And a = (-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
(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).