Question

point M is the midpoint of AB, point N is the midpoint of MB. find the ratios AM:MN, BN:AM, and MN:AB

Answer 1

Let, AB=4x unit

M is the midpoint of AB.

→AM=MB=2x unit---------Mid Point of segment divide it ino two equal parts.

Point N, is the midpoint of MB.

→MN=NB

MB=x unit

MN=NB=x unit---------Mid Point of segment divide it ino two equal parts.

`1.\rightarrow (MA)/(MN)=(2x)/(x)\\\\=2\\\\2.\rightarrow (BN)/(MA)=(x)/(2x)\\\\=(1)/(2)\\\\3.\rightarrow (MN)/(AB)=(x)/(4x)\\\\=(1)/(4)`

Answer 2

We know that:

• Point M is the midpoint of AB
• Point N is the midpoint of MB

Let AB be x

⇒ AM = MB =
`(x)/(2)`

and MN = NB =
`(x)/(4)`

Now, the ratios would be:

• AM:MN =
  `(x)/(2)` ÷
  `(x)/(4)` = 2
• BN:AM =
  `(x)/(4)` ÷
  `(x)/(2)` =
  `(1)/(2)`
• MN:AB =
  `(x)/(4)` ÷
  `(x)/(1)` =
  `(1)/(4)`