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Math Help - isometry

  1. #1
    Member Veronica1999's Avatar
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    isometry

    Consider a transformation T for which the image of the x-axis is the line 2x+3y=6 and the image of the y-axis is the line x+7y=7. What must be the image of the origin? Could T be an isometry?

    This seems simple but i am not sure of my answer.

    y=o y=-2/3x+2

    x=0 x= -7y+7

    origin (7,2)

    Is this an isometry?
    I don't think it is.
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  2. #2
    MHF Contributor
    Opalg's Avatar
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    Re: isometry

    The two axes intersect at the origin. If the transformation takes the axes to the two given lines, then it must take the origin to the point where those two lines intersect.

    The two axes are perpendicular to each other. If the transformation is an isometry, then it must take the axes to a pair of perpendicular lines. Are the two given lines perpendicular to each other?
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