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Math Help - basic geometry problem

  1. #1
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    basic geometry problem

    Help!
    Find the point of the line passing through A(-1,-1) and B(4,4) which is
    (a) twice as far from A as from B (two cases).
    (b) three times as far from B as from A (two cases).

    I also need to graph it..Thanks.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by cannon View Post
    Help!
    Find the point of the line passing through A(-1,-1) and B(4,4) which is
    (a) twice as far from A as from B (two cases).
    (b) three times as far from B as from A (two cases).

    I also need to graph it..Thanks.
    HI

    For (1) , The point , call it Q divides the line internally in the ratio of 2:1 and externally in the ratio of 2:-1 .

    Case 1 (internal) :

    Q=\left(\frac{(-1\times 1+4\times 2)}{2+1} , \frac{-1\times 1+4\times 2}{3}\right)

    Case 2: (external) : just flip the signs .

    (2) Q divides the line in a ratio of 1:3 , and 1:-3 . Use the formula again .
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  3. #3
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    I'm pretty confused with the ratios. In (a) the ratio is 2:1, shouldn't be (b) 1:3 but 3:1?
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