SOLUTION: If D is the midpoint of line AC and C is the midpoint of line AB, and AD is 3 cm., what is the length of AB?

Question 153973: If D is the midpoint of line AC and C is the midpoint of line AB, and AD is 3 cm., what is the length of AB?
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
If D is the midpoint of line AC and C is the midpoint of line AB, and AD is 3 cm., what is the length of AB?



Draw AC

@-----------@
A          C 

>>...D is the midpoint of line AC...<<

So put D in the middle of AC

@-----@-----@
A     D     C

>>...C is the midpoint of line AB...<<

So Extend AC twice its length to B so that C
will be in the middle of AB

@-----@-----@-----------@
A     D     C           B 

>>...AD is 3...<<
 
So put 3 on AD

   3
@-----@-----@-----------@
A     D     C           B 

Put another 3 on DC, because DC is the same length as AD.


   3     3
@-----@-----@-----------@
A     D     C           B

That makes AC have length 3+3 or 6.

Since CB is the same length as AC, we write
6 on CB


   3     3        6
@-----@-----@-----------@
A     D     C           B

Add up the pieces

AB = AD + DC + CB = 3 + 3 + 6 = 12.

Edwin

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