
transformations
hello, need a few pointers please.
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)
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)
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) =
http://www.mathhelpforum.com/mathhe...1049f23c1.gif + http://www.mathhelpforum.com/mathhe...e13b342d1.gif
For b)
I found that (f = Ax + a) f(x) =
http://www.mathhelpforum.com/mathhe...b7c8924a1.gif + http://www.mathhelpforum.com/mathhe...210e00cd1.gif
any help with part c and d would be great
many thanks
wayne

Hi,
there is a thread already here which i have posted on and I have posted i'm stuck on part (c) if you can help with this bit
nev
http://www.mathhelpforum.com/mathhe...ormations.html

Part C is solved by using the formula.
g o f (x)= g(f(x)) = B(Ax+a)+b = BAx+Ba+b
if you plug in the results of the matrices and vectors found in parts (a) and (b) for f(x) =Ax+a and g(x)=Bx+b then you should find the solution