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Math Help - Coordinate Geometry

  1. #1
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    Exclamation Coordinate Geometry

    Given that the points A(a,a+1), B (-6, -3) and C (5,-1), find the possible values of a if the length of AB is twice the length of AC.
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  2. #2
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    What did you get? How did you get it?
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  3. #3
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    I used the distance formula but am not able to get the correct answer.
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  4. #4
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    Quote Originally Posted by Ilsa View Post
    I used the distance formula but am not able to get the correct answer.
    Well, let's see:
    AB = SQT{[a - (-6)]^2 + [a+1 - (-3)]^2} = SQRT[(a + 6)^2 + (a + 4)^2]

    AC = SQT{[a - 5]^2 + [a+1 - (-1)]^2} = SQRT[(a - 5)^2 + (a + 2)^2]

    Since AB = twice AC:
    SQRT[(a + 6)^2 + (a + 4)^2] = 2SQRT[(a - 5)^2 + (a + 2)^2]

    Square both sides:
    (a + 6)^2 + (a + 4)^2 = 4[(a - 5)^2 + (a + 2)^2]

    Did you follow that? Can you wrap it up?
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  5. #5
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    Quote Originally Posted by Ilsa View Post
    I used the distance formula but am not able to get the correct answer.
    This reply sheds no light at all on what you did and why your answer might be wrong. How are we to know what mistake(s) you have made? Working that clearly shows how you got your answer is obviously needed!
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