If there are two points m and N on the line AB, point m divides AB into two parts of 1:2, point n divides AB into two parts of 2:1, and Mn = 4cm, then am=______ cm，BN=______ cm．

If there are two points m and N on the line AB, point m divides AB into two parts of 1:2, point n divides AB into two parts of 2:1, and Mn = 4cm, then am=______ cm，BN=______ cm．

As shown in the figure, ∵ point m divides AB into two parts of 1:2, and point n divides AB into two parts of 2:1, ∵ points m and N are the three equal points of line AB, ∵ am = Mn = BN, ∵ Mn = 4cm, ∵ am = 4cm, BN = 4cm

It is known that there are two points m and N on the line ab. point m divides AB into two parts 2:3 and point n divides AB into two parts 4:1. If Mn = 3cm, the length of AM and Nb can be obtained

∵ point m divides AB into 2:3 parts, ∵ am = 25ab; ∵ point n divides AB into 4:1 parts, ∵ an-am = Mn, ∵ 45ab-25ab = 3, ∵ AB = 7.5cm, ∵ am = 25ab = 3cm. ∵ NB = ab-an = 15ab = 1.5cm. So am = 3cm, Nb = 1.5cm

Given that the line segment AB = 10cm, the point m is on the line AB, am = 4cm, and N is the midpoint of MB, then the line segment Mn=______ cm．

∵ line AB = 10cm, point m is on line AB, am = 4cm, ∵ MB = 6cm, and N is the midpoint of MB, so Mn = 12MB = 12 × 6 = 3cm