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.
determine g (in the form g(x) Ax + a, where A is a 2x2 matrix and a is a vector with two components.
Express 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)).
Fine the affine transformation g o f (in the same form as you found g in part a)).
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.