*f*and

*g*are both affine transformations. The

transformation

*f*is reflection 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 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 you found

*g*in

part (a).

*I have answers to these questions but I'm really not sure if they're right, so if someone could put up the correct answers so I can see how I did then that would be great! Thanks*