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math

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The image of the point (1, -2) after a rotation of 180° about the origin is

  • math -

    (-1,+2) by inspection

    using 90 deg matrix
    R90 =
    |+0 -1|
    |+1 +0|
    R180 is R90 * R90
    |+0 -1||+0 -1|
    |+1 +0||+1 +0|
    which is
    |-1 +0|
    |+0 -1|

  • continued -

    |-1 +0| |+1|
    |+0 -1| |-2|

    = (-1, +2 )

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