1. ## 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.

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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

2. OK for 1 but AC/BC=1

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