(a) The affine transformation f maps the points (0,0), (1,0) and (0,1) to the points (4,4), (3,4) and (4, 5), respectively. (i) Determine f in the form f(x) = Ax + a, where A is a 2 X 2 matrix and a is a column vector with two components. [2] (i) Find the fixed points (if any) of f, and state whether f is a translation, rotation, reflection or glide-reflection. [3] (b) The affine transformation k is the anticlockwise rotation through /2 about the point (3, 4). By using the translation h that maps the point (3, 4) to the origin, and its inverse A~ !, find the transformation k in the form k(x) = Bx + b, where B is a 2 x 2 matrix and b is a column vector with two components. 5]