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Math Help - Affine Transformations

  1. #1
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    Affine Transformations

    Hi all so ive read all my books and tried searching online and also discussing with my professor but i am still not getting this

    if anyone could answer and explain for me i would really appreciate it

    in this question 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 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) find the images of the points (0,0), (1,0) and (0,1) under the composite affine transformation g - f
    (that is f followed by g)

    d) hence or otherwise find the affine transformation g - f in the same form as you found g in part a)

    e) use your answer to part d) to show that there is exactly one point (x,y) such that the image of (x,y) under g-f is (x,y). state the co-ordinates of this point

    f)given that g -f is a rotation about the point described in part e) find the angle of rotation (including its sign)



    even if you are able to give pointers and not answers id be really grateful

    thanks guys
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  2. #2
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    Re: Affine Transformations

    Hi,
    I hope the following helps. I left a few details for you.



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