Segments problem: C is the midpoint of AB, D is the....

[alee]

Please help me get started:

Point C is the midpoint of AB, D is the midpoint of AC, E is the midpoint of CB and F is the midpoint of DB. If CF =x, find the length of DA and FB in terms of x.

Thank you.

 

[jonboy]

Once again make a drawing. Here is what I get in terms of \(\displaystyle x\):

Wait till someone comes along and checks it because I am not 100% sure.

 

[soroban]

Re: Segments problem

Hello, alee!

Jonboy is absolutely correct.

Here's my baby-talk approach . . .

Suppose the length of \(\displaystyle AB\) is \(\displaystyle 8.\)

Point C is the midpoint of AB

      |       4       |       4       |
      *---------------*---------------*
      A               C               B

D is the midpoint of AC

      |   2   |   2   |       4       |
      *-------*-------*---------------*
      A       D       C               B

E is the midpoint of CB

      |   2   |   2   |   2   |   2   |
      *-------*-------*-------*-------*
      A       D       C       E       B

F is the midpoint of DB.

      |   2   |   2   | 1 | 1 |   2   |
      *-------*-------*---*---*-------*
      A       D       C   F   E       B

If \(\displaystyle CF\,=\,x\), find the length of \(\displaystyle DA\) and \(\displaystyle FB\) in terms of \(\displaystyle x\)

And we see that: \(\displaystyle \,\begin{array}{ccc}DA\:=\:2\,\times CF\\. \\FB\:=\:3\,\times\,CF\end{array}\)

 

[jonboy]

Yeah I felt pretty confident on my anwer. Thank you Soroban for your approach because mine was not to explainable.