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Math Help - parallelogram

  1. #1
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    parallelogram

    Three vertices of a parallelogram are (1,1), (3,5), and (-1,4) . find all possible ordered pairs that could be the coordinates of the fourth vertex .
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  2. #2
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    (-3,0), (5,2), (1,8)
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  3. #3
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    Hello, sri340!

    Three vertices of a parallelogram are: A(1,1), B(3,5), and C(-1,4).
    Find all possible ordered pairs that could be the coordinates of the fourth vertex .
    This can be solved without any fancy formulas . . .
    Code:
              |           B
              |         (3,5)
              |           o
              |     *    *  *
        C     *         *     *
        o     |        *        *
    (-1,4)*   |       *           *
            * |      *              o D
              *     *         *
              | *  *    *
              |   o
              | (1,1)
              |   A
    - - - - - + - - - - - - - - - - - - -
              |

    Suppose vertex D is to the right, as shown in the diagram.

    Going from C to B, we move: right 4, up 1.

    Since AD \parallel CB, going from A to D, we make the same moves.

    Therefore: . A(1,1) + (\text{right 4, up 1}) \;=\;D(5,2)


    There are two more possible locations for vertex D:
    . . left and above \Delta ABC, and left and below \Delta ABC.

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