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Math Help - Translation

  1. #1
    Senior Member Mukilab's Avatar
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    Translation

    How does one 'Describe fully a single translation'?

    My object has been reflected twice, do I just say 'reflected on x=_ then on y=_'?
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Combining two reflections

    Hello Mukilab
    Quote Originally Posted by Mukilab View Post
    How does one 'Describe fully a single translation'?

    My object has been reflected twice, do I just say 'reflected on x=_ then on y=_'?
    Are you sure the question says 'a single translation'? The combined transformation will be a translation only if the two mirror-lines are parallel. And from what you say about ' x =... ' and ' y =...', it sounds as if they aren't.

    Does the question say 'Describe fully a single transformation ...'?

    When one reflection is followed by a second reflection in mirror-lines that are not parallel, this is equivalent to a rotation, whose centre is at the point where the mirror-lines meet, through twice the angle between them.

    It sounds as if your mirror-lines are at right-angles, so the rotation will be through a half-turn.

    Does that help to answer your question?

    Grandad
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  3. #3
    Senior Member Mukilab's Avatar
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    It can't just be a rotation, it doesn't make sense.

    It is 'single transformation'


    Here are the coordinates of the three triangles
    A= 0,3 1,3 and 1,5
    B= 3,0 3,1 and 5,1
    C= 5,3 6,3 and 5,5

    Describe the translation of A onto B. Is this a reflection around line y=x?
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  4. #4
    MHF Contributor
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    Hello Mukilab
    Quote Originally Posted by Mukilab View Post
    It can't just be a rotation, it doesn't make sense.

    It is 'single transformation'


    Here are the coordinates of the three triangles
    A= 0,3 1,3 and 1,5
    B= 3,0 3,1 and 5,1
    C= 5,3 6,3 and 5,5

    Describe the translation of A onto B. Is this a reflection around line y=x?
    Again, you have used the word 'translation' when you meant 'transformation'.

    I was guessing what the answer might be, based on the incomplete information you gave me in your first post. You are right: the transformation that maps A onto B is a reflection in the line y = x.

    B is then mapped onto C by a rotation through 90^o anticlockwise, centre (3,3).

    The single transformation that maps A onto C is a reflection in the line x = 3.

    Grandad
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