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Math Help - Analytic Geometry Q5

  1. #1
    Member looi76's Avatar
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    Analytic Geometry Q5

    Question:
    Show the points A(-1,0) , B(5,2) , C(8,7) & D(2,5) are vertices of a parallelogram.

    I don't what I'm suppose to find the prove that it's a parallelogram. Should I find the slope m of the lines? or should I find the distance between the points? and what does vertices mean?!

    EDIT: This question is related to the lesson of Inclination and Slope of a line.
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  2. #2
    MHF Contributor red_dog's Avatar
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    Yes, you have to find the slope of the lines and see that

    m_{AB}=m_{CD} and m_{BC}=m_{AD}
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  3. #3
    Member looi76's Avatar
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    A(-1,0) , B(5,2) , C(8,7) & D(2,5)

    Slope of line AB:

    A(-1,0) & B(5,2)

    m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2-0}{5-(-1)} = \frac{1}{3}


    Slope of line CD:

    C(8,7) & D(2,5)

    m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5-7}{2-8} = \frac{1}{3}


    Slope of line BC:

    B(5,2) & C(8,7)

    m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7-2}{8-5} = \frac{5}{3}


    Slope of line AD:

    A(-1,0) & D(2,5)

    m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5-0}{2-(-1)} = \frac{5}{3}


    So, this is the answer?
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  4. #4
    MHF Contributor red_dog's Avatar
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    If m_{AB}=m_{CD}\Rightarrow AB\parallel CD

    and if m_{BC}=m_{AD}\Rightarrow BC\parallel AD

    So ABCD is a parallelogram.
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