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Math Help - Lines?

  1. #1
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    Lines?

    If A, B, C, and D lie on the same straight line, and if AC = 2CD = 3BD, what is the value of the ratio BC/CD ?

    The answer says/explains:
    Let AC = 6; then CD = 3, with D on either side of C. BD=2, but B could be on either side of D, and so we have no way of knowing length BC. The value of the ratio BC/CD cannot be determined from the information given.

    I don't understand how they came to that conlucsion.

    AND why are there 2 D'S?! "D on either side of C"??
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  2. #2
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    Points on a line

    Hello juliak
    Quote Originally Posted by juliak View Post
    If A, B, C, and D lie on the same straight line, and if AC = 2CD = 3BD, what is the value of the ratio BC/CD ?

    The answer says/explains:
    Let AC = 6; then CD = 3, with D on either side of C. BD=2, but B could be on either side of D, and so we have no way of knowing length BC. The value of the ratio BC/CD cannot be determined from the information given.

    I don't understand how they came to that conlucsion.

    AND why are there 2 D'S?! "D on either side of C"??
    Have a look at the diagram I've attached.

    The question doesn't say that the points A, B, C and D are in that order along the line. They might be in the order A, C, D, B for instance.

    So if AC = 6 units and CD = 3, then there are two possible positions for D - one on either side of C. I've called these D_1 and D_2.

    In the same way, for each of the possible positions of D, there are 2 possible positions for B - 4 positions altogether. I've called these B_1 through B_4.

    Do you see why there are several possible answers now?

    Grandad
    Attached Thumbnails Attached Thumbnails Lines?-untitled.jpg  
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