Question

Point M is the midpoint of AB ; point N is the midpoint of MB. Find the ratios of AM : MN, BN : AM, MN : AB

Answer 1

Let's assume that AB is a line segment with length 2x. This means that AM and MB have lengths x each.

Since M is the midpoint of AB, the length of AM is equal to the length of MB.

Therefore, AM = MB = x.

Since N is the midpoint of MB, the length of MN is half of the length of MB.

Therefore, MN = 0.5x.

Now, we can find the ratios:

1) Ratio of AM to MN: AM : MN = x : 0.5x = 2 : 1

2) Ratio of BN to AM: BN : AM = x : x = 1 : 1

3) Ratio of MN to AB: MN : AB = 0.5x : 2x = 1 : 4

So, the ratios are:

1) AM : MN = 2 : 1

2) BN : AM = 1 : 1

3) MN : AB = 1 : 4