AD= 36 cm. Points C, B∈AD, such that AB:BC:CD=2:3:4. Find the distance of midpoints of the segments AB and CD.

We have  (2 + 3 + 4)  =  9  equal parts of  AD

Let A  = (0,0)    and  let D  = (36,0)

Then    AB  =  (2/9) (36)  =   8

So    B  =(8, 0)

And the   midpoint  of AB   =   (4,0)

And AC  is   (2 + 3)  /  9    =   (5/9)  of AD =  (5/9) (36)   =  20

So  C  =  (20,0)

And the midpoint  of CD  =   [ (20 +36)  / 2  , 0  ]  =   [  56 / 2  ,  0  ]   =  (28,0)  

So  the distance between  the midpoint  of AB  and the  midpoint  of CD = 28  - 4  =  24