I would be grateful to anyone who can help me with this!
In this question, f and g are both affine transformations. The transformation f is 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 2 x 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) find 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 briefly.