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Math Help - Find the possible value for a.

  1. #1
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    Find the possible value for a.

    Given the points A(a, 3), B(-2, 1) and C(3, 2), find the possible value of a if the length of AB is twice the length of BC.
    Thanks.
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  2. #2
    Member rtblue's Avatar
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    Mar 2009
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    Birmingham, Alabama.
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    using the distance formula to find the length of BC we have:

    \displaystyle \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}

    \displaystyle \sqrt{(5)^2+(1)^2

    \displaystyle \sqrt{26}=BC

    using some algebra and the fact that AB will be twice BC:

    2\sqrt{26}=\sqrt{(a+2)^2+(2)^2}

    solve for a.
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  3. #3
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    Thanks so much for all of your help.
    I ended up getting a= -12 or 8, which is right. YAY!
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