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Math Help - transformations

  1. #1
    Junior Member
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    Mar 2009
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    west sussex
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    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) =


    +

    For b)

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


    +

    any help with part c and d would be great

    many thanks
    wayne
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  2. #2
    Newbie
    Joined
    Jun 2010
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    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

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  3. #3
    Newbie
    Joined
    Jun 2010
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    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
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