...in the line y=x-1 and the transformation g maps the points (0,0), (1,0) and (0,1) to the points (3,-1),(4,-1) and (3,-2) 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) 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).
c) find the images of the points (0,0), (1,0) and (0,1) under the composite affine transformation g - f
(that is f followed by g)
d) hence or otherwise find the affine transformation g - f in the same form as you found g in part a)
e) use your answer to part d) to show that there is exactly one point (x,y) such that the image of (x,y) under g-f is (x,y). state the co-ordinates of this point
f)given that g -f is a rotation about the point described in part e) find the angle of rotation (including its sign)
i have no idea on any of this so an explanation of how to do it would very much be appreciated