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Thread: Line segments

  1. #1
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    Line segments

    Given line segment $\displaystyle AB$,

    1.) Where should one place point $\displaystyle C$ such that the ratio of the length of $\displaystyle AB$ to the length of $\displaystyle AC$ is $\displaystyle 2$? When $\displaystyle C$ is in this position, what's the ratio of the length of $\displaystyle AC$ to $\displaystyle BC$?

    2.) Where should one place point $\displaystyle C$ such that the ratio of the length of $\displaystyle AB$ to the length of $\displaystyle AC$ is $\displaystyle 1$? Are you able to determine the ratio of $\displaystyle AC$ to $\displaystyle BC$? If so, find it. If not, explain why not.

    3.) Using your answers from #1 and #2, determine the smallest and largest possible numbers for the ratio of the length of the whole to the length of the greater -- that is, the length of the whole is AB and the greater will be the bigger line segment cut but C.

    ---

    My solutions:

    For #1:

    I would put C in the middle- this would make the ratio 2. The value of AC/BC would be 1/2.

    For #2:

    I would put C where B is. Then it's 1. Then AC/BC would be 1 too would it not? I think?

    For #3: Not sure
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  2. #2
    MHF Contributor
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    OK for 1 but AC/BC=1

    OK for 2 but B=C means BC=0 so ...
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