# transformations

• Jun 3rd 2010, 09:55 AM
smartcar29
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/math-he...1049f23c-1.gif + http://www.mathhelpforum.com/math-he...e13b342d-1.gif

For b)

I found that (f = Ax + a) f(x) =

http://www.mathhelpforum.com/math-he...b7c8924a-1.gif + http://www.mathhelpforum.com/math-he...210e00cd-1.gif

any help with part c and d would be great

many thanks
wayne
• Jun 3rd 2010, 10:40 AM
Tinca18
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/math-he...ormations.html
• Jun 4th 2010, 03:39 AM
Tinca18
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