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Math Help - paralleogram

  1. #1
    Newbie Zharif93's Avatar
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    [SOLVED]parallelogram

    P(-3,2) Q(2,-2) R(3,1) S(x,y) are the vertices of a parallelogram .Find
    the values of x and y
    Last edited by Zharif93; July 15th 2010 at 09:32 PM.
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  2. #2
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    Hello Zharif,
    This is an oft repeated problem so you could scan thru current and past answers. For immediate help try this.

    Plot the three points.Connect PR ang RQ. Note that two parallelograms can be constructed where x,y are in different quadrants.Draw a line thru P approx parallel to RQ. What is the slope of this line .x,y must lie on it. Proceed and report.


    bjh
    Last edited by bjhopper; July 15th 2010 at 04:24 AM. Reason: spelling
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  3. #3
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    Hello, Zharif93!

    Did you make a sketch?
    The answer jumps out at you!


    P(\text{-}3,2),\;Q(2,\text{-}2),\;R(3,1),\; S(x,y) are the vertices of a parallelogram.
    Find the values of x and y
    Code:
               S        |
             (x,y)o     |
                 /↑  *  |
                / ↑     *
               /  ↑     |  *
              /   ↑     |     *
         P   /    ↑     |        *      R
      (-3,2)o → → +     |           o (3,1) 
               *        |          *↑
      - - - - - - * - - + - - - - * ↑ - - - -
                     *  |        *  ↑ 3
                        *       *   ↑
                        |  *   * 1  ↑
                        |     o → → +
                        |  (2,-2)
                        |     Q

    Assuming that parallelgram PQRS has its vertices in order,
    . . we see that vertex S is in the upper-left.

    Going from Q to R, we move 1 unit right, 3 units up.

    Since PS \parallel QR, going from P to S,
    . . we also move 1 unit right, 3 units up.


    Therefore, vertex S is at (-2,5).

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