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Math Help - Find a coordinate of a Paralellogram?

  1. #1
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    Find a coordinate of a Paralellogram?

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  2. #2
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    Hello, rcfreak339!

    I don't suppose you made a sketch . . .


    ABCD is a parallelogram
    with vertices: . A(-2,1),\;B(2,-2),\;C(8,7),\;D(x,y)

    (a) Find the coordinates of point D.
    Code:
                  |   D
                  |   o
                  |   :
                  |   :           C
                  |   :           o (8,7)
                  |   :           :
         (-2,1)   |   :           :
          A o - - | - *           :9
        - - - - - + - - - - - - - : - - -
                  |               :
                  |   B o - - - - *
                  |  (2,-2)  6
                  |

    Since ABCD lists the vertices in order,
    . . the diagram shows the position of vertex D.

    Going from B to C, we move right 6, up 9.

    Since AD is parallel to BC, we must do the same from vertex A.

    Moving "right 6, up 9" from (-2,1) puts us at: . D(4,10).




    (b) Determine if parallelogram ABCD is a rectangle.
    Compare the slopes of AB and BC.

    . . m_{_{AB}} \:=\:\frac{-2 - 1}{2-(-2)} \:=\:-\frac{3}{4}

    . . m_{_{BC}} \:=\:\frac{7-(-2)}{8-2} \:=\:\frac{9}{6} \:=\:\frac{3}{2}


    The slopes are not negative reciprocals of each other.

    Hence, AB is not perpendicular to BC\!:\;\;\angle B \,\neq\,90^o

    Therefore, ABCD is not a rectangle.

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  3. #3
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    ^Thank you for the very informed and helpful post! I just am not very good at graphing and such, I can do Algebra any day but when t comes to Coordinates I am just not good...
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