Hi,

I would be grateful to anyone who can help me with this!

In this question,fandgare both affine transformations. The transformationfis reflection in the linex =2, and the transformationgmaps the points (0, 0), (1, 0) and (0, 1) to the points (0, -4), (0, -3) and (-1, -4) respectively.

(a) Determineg(in the form g(x) =Ax+a, whereAis a 2 x 2 matrix andais a vector with two components).

(b) Expressfas a composite of three transformations: a translation, followed by reflection in a line through the origin, followed by a translation. Hence determinef(in the same form as you foundgin part (a)).

(c) find the affine transformation g of(in the same form as you foundgin part (a)).

(d) Given that g ofis 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.

Many thanks