Given the line AB = 10, C is any point on the line AB, M is the midpoint of AC, n is the midpoint of BC, find the length of Mn No graph, standard process, all three solutions

Given the line AB = 10, C is any point on the line AB, M is the midpoint of AC, n is the midpoint of BC, find the length of Mn No graph, standard process, all three solutions

There should be three situations
1. Point C is on line AB, excluding points a and B
MN=MC+CN
=1/2AC+1/2BC
=1/2(AC+BC)
=1/2AB
=5
2. C coincides with points a and B
MN=0
3. Point C is outside line ab
The length of Mn is more than 5
Am I forgetting

C is any point on the line AB, M is the midpoint of AC, and N is the midpoint of BC. If AB = 10cm, the length of line Mn is

5 cm if M is on point a

Line AB = 10cm, C is any point on line AB, M is the midpoint of BC, and the length of Mn is calculated

A -- m -- C -- N -- B we know: ab = 10, am = MC, CN = NB find Mn, let am be x, cn be y, because am = MC = x, CN = NB = y, AC = am + MC = 2x, CB = CN + Nb = 2yac + CB = AB, so 2x + 2Y = AB = 102 (x + y) = 10, x + y = 5, x + y = am + CN = MC + CN