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Thread: 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 . . .


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

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

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

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

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

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




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

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

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


    The slopes are not negative reciprocals of each other.

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

    Therefore, $\displaystyle ABCD$ 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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