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January 31st, 2012, 06:24 AM   #1
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affine transformations

Hey all! hope all is well! this question is quite long, and leads on from one another, i'm just stuck on the second part, if anyone could explain thanks!

In this question, f and g are both affine transformations. The
transformation f is reflection in the line y = 2, and the transformation g
maps the points (0, 0), (1, 0) and (0, 1) to the points (1, 1), (2, 2) and
(3,?1), respectively.

(a) Determine g (in the form g(x) = Ax + a, where A is a 22 matrix
and a is a vector with two components).

Done this part which equals g(x) = (matrix) x + (vector) the matrix is (a,b,c,d) (1,2,1,-2) vector (a,b) (1,1)

the next part i don't understand

(b) Express f as a composite of three transformations: a translation,
followed by 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 understand what u have to do here and the process u need to take, but i can't understand if y=2 then surely it will be parallel with the x axis, which wont make an angle which u need for the formula of a reflection matrix (a = cos(2phi) b= sin(2phi) c= sin(2phi) d= -cos(2phi))
fe phi fo is offline  
 
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