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

We know that:

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

Let AB be x

⇒ AM = MB = $\frac{x}{2}$

and MN = NB = $\frac{x}{4}$

Now, the ratios would be:

• AM:MN = $\frac{x}{2}$ ÷ $\frac{x}{4}$ = 2
• BN:AM = $\frac{x}{4}$ ÷ $\frac{x}{2}$ = $\frac{1}{2}$
• MN:AB = $\frac{x}{4}$ ÷ $\frac{x}{1}$ = $\frac{1}{4}$

Answer 2

Solution

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.

$1.\rightarrow \frac{MA}{MN}=\frac{2x}{x}\\\\=2\\\\2.\rightarrow \frac{BN}{MA}=\frac{x}{2x}\\\\=\frac{1}{2}\\\\3.\rightarrow \frac{MN}{AB}=\frac{x}{4x}\\\\=\frac{1}{4}$