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Math Help - Vertices of a parallelogram?

  1. #1
    Newbie oXCryssieLeahXo's Avatar
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    Unhappy Vertices of a parallelogram?

    Goodness I don't understand this at all!!! I understand finding the coordinates of a parallelogram, but this makes no sense.

    So it says "Which of the set of points cannot be the vertices of parallelogram ABCD?"

    options are

    a) A (-4, -2), B (2, 0), C (3, 3), D (-2, -1)

    b) A (-2, -1), B (3, -2), C (4, 1), D (-1, 2)

    c) A (0, -2), B (4, -1), C (5, 2), D (0, 5)

    d) A (0, -2), B (5, -3), C (7, 1), D (2, 2)

    so can someone tell me what formula to use to find the answer? (I'm assuming there's a formula!)
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  2. #2
    Super Member
    earboth's Avatar
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    Quote Originally Posted by oXCryssieLeahXo View Post
    ...

    So it says "Which of the set of points cannot be the vertices of parallelogram ABCD?"

    options are

    a) A (-4, -2), B (2, 0), C (3, 3), D (-2, -1)

    b) A (-2, -1), B (3, -2), C (4, 1), D (-1, 2)

    c) A (0, -2), B (4, -1), C (5, 2), D (0, 5)

    d) A (0, -2), B (5, -3), C (7, 1), D (2, 2)

    ...
    The properties of a parallelogram are:

    1. The diagonals have a common midpoint.
    2. 2 pairs of parallel sides
    3. The parallel sides have the same length (#3 is equivalent to #2)

    First check if
    M_{AC} = M_{BD}

    So only b) and d) could be a parallelogram

    Check if

    (\overline{AB})\ \parallel \ (\overline{CD})

    only d) is left. Since \left(\begin{array}{c}-5\\1\end{array}\right) = k \cdot \left(\begin{array}{c}5\\-1\end{array}\right) the sides (\overline{AB})\ \parallel \ (\overline{CD})

    PS: Fröhliche Ostern!
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  3. #3
    Newbie oXCryssieLeahXo's Avatar
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    Smile Thank yah

    Quote Originally Posted by earboth View Post
    The properties of a parallelogram are:

    1. The diagonals have a common midpoint.
    2. 2 pairs of parallel sides
    3. The parallel sides have the same length (#3 is equivalent to #2)

    First check if
    M_{AC} = M_{BD}

    So only b) and d) could be a parallelogram

    Check if

    (\overline{AB})\ \parallel \ (\overline{CD})

    only d) is left. Since \left(\begin{array}{c}-5\\1\end{array}\right) = k \cdot \left(\begin{array}{c}5\\-1\end{array}\right) the sides (\overline{AB})\ \parallel \ (\overline{CD})

    PS: Fröhliche Ostern!

    wow thank you SO much. Makes sense. I kinda feel dumb now that I didn't figure that out myself!!


    Frohe Ostern an dir auchh! =]]
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  4. #4
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    Hello, oXCryssieLeahXo!

    I don't suppose you tried to PLOT the points . . .


    Which of the set of points cannot be the vertices of parallelogram ABCD?

    . . a)\;A (\text{-}4, \text{-}2),\;B (2, 0),\;C (3, 3), D\;(\text{-}2, \text{-}1)
    Code:
                                |           C
            .   .   .   .   .   +   .   .   o   .
                                |
            .   .   .   .   .   +   .   .   .   .
                                |
            .   .   .   .   .   +   .   .   .   .
                                |
          - + - + - + - + - + - + - + - o - + - + -
                        D       |       B
            .   .   .   o   .   +   .   .   .   .
                                |
            .   o   .   .   .   +   .   .   .   .
                A               |
    No, I don't think so . . .

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