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Math Help - Coordinate geometry question.

  1. #1
    Ife
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    Coordinate geometry question.

    P - (-1, 11), Q - (2,5), R - (-2, 3). Angle PQR = 90 degrees. The line PQ is produced to S, so that QS = PQ. Calculate the coordinates of S.
    Idk why I am not getting this out... please help..

    thanks
    Last edited by mr fantastic; October 8th 2011 at 03:33 AM. Reason: Title.
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    Re: simple coordinate geometry question that is stumping me for some strange reason

    Quote Originally Posted by Ife View Post
    P - (-1, 11), Q - (2,5), R - (-2, 3). Angle PQR = 90 degrees. The line PQ is produced to S, so that QS = PQ. Calculate the coordinates of S.
    Idk why I am not getting this out... please help..

    thanks
    1. Draw a sketch!

    2. Let \overrightarrow{OP} = \vec p = \langle -1, 11 \rangle

    \overrightarrow{OQ} = \vec q = \langle 2, 5 \rangle

    3. \overrightarrow{PQ} = \vec q - \vec p = \langle 3,-6 \rangle = \vec d

    4. \overrightarrow{QS} = \vec q + \vec d = \langle 5, -1 \rangle

    5. Therefore the point S has the coordinates S(5, -1)
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    Re: simple coordinate geometry question that is stumping me for some strange reason

    another method. Given P,Q and PQ=QS no further info is required.Slope of PQ =-6/3 = slope of QS.S is then 3 units right ofQ and 6 units down from Q (5,-1)
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    Ife
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    Re: simple coordinate geometry question that is stumping me for some strange reason

    Quote Originally Posted by bjhopper View Post
    another method. Given P,Q and PQ=QS no further info is required.Slope of PQ =-6/3 = slope of QS.S is then 3 units right ofQ and 6 units down from Q (5,-1)
    thanks, but moving 3 across and 6 down to (5, -1) guarantees that QS = PQ?
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    Re: simple coordinate geometry question that is stumping me for some strange reason

    Hello, Ife!

    Thanks, but moving 3 across and 6 down to (5, -1) guarantees that QS = PQ?

    Yes, it does!

    Moving from P(\text{-}1.11) to Q(2,5), we move 3 right and 6 down.

    Moving from Q(2,5) to S(5,\text{-}1), we move 3 right and 6 down.

    The distances are equal . . . aren't they?

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