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Thread: Transformations

  1. #1
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    Transformations

    I have been puzzling over this question for some time.
    I've played about with it using GeoGebra but I really have no idea how to do it :/
    Any help would be much appreciated, thanks in advance )

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  2. #2
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    Re: Transformations

    Hey Melody2.

    Can you show us what you have tried? Have you tried making the answer visual [i.e. drawing it]?
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    Re: Transformations

    Thanks for your response Chiro,
    Yes I have.
    I drew it in Geogebra and subsequently learned how to do all the required transformations (dilation, refection and rotation in GeoGebra) but I do not know how to put them together to get the required solution.
    I tried uploading my basic pic, I haven't done that before either so I will see it it works.
    This is the link.
    https://ggbm.at/ckGVpWsb

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    Re: Transformations

    What about the attempts for the rotations and dilations?
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    Re: Transformations

    Yes I tried lots but none worked. I have no idea how to attack the problem logically.
    What is the point in putting up lots of random transformations?
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    Re: Transformations

    When you rotate around a point you subtract the point and then rotate the point counterclockwise by some angle.

    Have you looked at sines and cosines before?
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    Re: Transformations

    You are being very cryptic chiro and so far it is not helping.
    I never was any good at deciphering codes.
    Last edited by Melody2; Feb 19th 2017 at 12:59 AM. Reason: spelling error
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    Re: Transformations

    Quote Originally Posted by Melody2 View Post
    You are being very cryptic chiro and so far it is not helping.
    I never was any good at deciphering codes.
    I really do not think that Chiro is being only cryptic, but rather helping you think about the problem.

    I have not tried helping because the question as written make no sense to me.
    There is a well-known transformation across the y-axis: (x,y) \to (x',y') = \left\{ \begin{array}{l}x' =  - x\\y' = y\end{array} \right.

    All to other instructions have nothing to do with th transformation as far as I am concerned.
    Thanks from topsquark
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    Re: Transformations

    Quote Originally Posted by Melody2 View Post
    You are being very cryptic chiro and so far it is not helping.
    I never was any good at deciphering codes.
    I agree with Plato. In addition to his (Plato's) comments, Chiro is giving you a list of transformations you want to look for.

    -Dan
    Last edited by topsquark; Feb 19th 2017 at 05:58 AM.
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    Re: Transformations

    I'm not being cryptic - take a look at the rotation matrix in two dimensions for more information.
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    Re: Transformations

    Let's see what we have here:
    Plato says :"the question as written make no sense to me"
    topsquark says "I agree with Plato."

    The wording of the questions makes total sense to me except that perhaps it is not doable.
    Thanks guys.
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    Re: Transformations

    Quote Originally Posted by Melody2 View Post
    The wording of the questions makes total sense to me except that perhaps it is not doable.
    Now I agree completely with that.
    The OP shows a figure and its image reflected about the y-axis. Then the question proceeds to ask for a sequence of transformations to accomplish that simple reflection. There is no reason for rotations, reflection about y=x, or dilations. Tell us how does that makes sense to you? The question asks for one simple transformation: reflection about the y-axis.
    Thanks from topsquark
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    Re: Transformations

    I would like to tell you gentlemen a story.

    A peasant girl is given a spinning wheel. She has been using one of these since she was a little girl so she knows how it works.
    She is also given a room full of straw.
    She is told that to save he father’s life she must spin the straw into gold.

    Does she understand her task? Absolutely she does. She is expected to spin the straw into gold. The instructions are in plain English.
    Can she do it? No she does not know how.

    She asks the wise owl if he knows how it is done. He peers at her over the top of his spectacles and says "Arr go learn to make brass, copper and zinc be the substances needed.” The poor girl is no closer to spinning the gold but a kindly mouse says, “The owl is wise, follow his lead. The task makes no sense but the owl will not misguide you.”
    The girl is more confused than ever, she trusts the mouse and the owl, they have told her what she must learn to complete her task but they have also told her that the task is probably not doable and it makes no sense in the first place.

    Then the girl discovers the real problem. She has fallen down the rabbit hole and her name is Alice. Her instructions were given to her by the mad hatter. All she has to do is to climb out of the rabbit hole and her father will be safe.

    Arr Don’t you love happy endings
    Thanks from topsquark
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    Re: Transformations

    Thank you Topsquark for appreciating my humour.
    -------------------

    A note to all the answerers on this thread:

    I presented you with a well written problem. None of you could answer it.
    You could have:
    1) Ignored it.
    2) Admitted you did not know the answer and suggest that it may not be doable.

    But no, you chose to ridicule the question and humiliate me instead.
    You all should be ashamed of yourselves!
    It is not clever to treat question askers with such condescension. It is just plain rude.
    You should have respect for the hard working, mathematics loving, questions presenters who keep you all so entertained!

    Plato derisively asked:
    “The OP shows a figure and its image reflected about the y-axis. Then the question proceeds to ask for a sequence of transformations to accomplish that simple reflection. There is no reason for rotations, reflection about y=x, or dilations. Tell us how does that makes sense to you? “

    Well Plato, we are often asked how we can do things another way and, for this question, this is how:

    It only takes 4 steps.
    1) Reflect over y=x
    2) Dilate to a factor of 2 about (-5,0)
    3) Rotate 90 degrees anticlockwise about (5,0)
    4) Dilate to a scale factor of 0.5 about (-5,0)

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    Re: Transformations

    I'm curious how you were able to figure this out. After toying with it for a while I suspected you'd need to move the shape off of (5,0) and rotate it but I wouldn't have come up with that dilation trick in a million years.
    Thanks from Plato and Melody2
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