f and g are both affine transformations, the transformation f is reflection in the line y=2, and the transformation g maps the points (0,0), (1,0) and (0,1) to the points (1,1), (2,2) and (3,-1) 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 a reflection in a line through the origin, followed by a translation. Hence determine f (in the same form as found g in part (a))
(c) Use the expression found for f(x) and g(x) in parts (a) and (b) to calculate f(g(x)), and hence find the affine transformation f o g, in the same for as you found g in part (a)
(d) Use your answer to part (c) to determine any points (x,y) that are left unchanged by the transformation f o g, or show that there are no such points (find any values of x and y for which f(g(x,y)) = (x,y))
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