Hi, the complete original question is:
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.
a) determine g (in the form g(x) Ax + a, where A is a 2x2 matrix and a is a vector with two components.
b) Exprerss 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)).
c) Fine 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.
For a) I found that (g = Bx + b) g(x) =
For b) I found that (f = Ax + a) f(x) =
c) I am unsure how to combine the two answers above. I thought something like: (?)
g o f = g(f(x))
= g(Ax + a)
= B(Ax + a) + b
d) Also I am not sure how to work out this question.
Any help would be much appreciated. Thanks for your help in advance.