Given that point C is a point on line AB, ab = 12cm, AC: BC = 1:3, and point m is the midpoint of line BC, find the length of line am

Given that point C is a point on line AB, ab = 12cm, AC: BC = 1:3, and point m is the midpoint of line BC, find the length of line am

The length of AM is 7.5cm
Line ab12cm AC: BC = 1:3
So ac3cm bc9
M is the midpoint of BC, CM 4.5cm
AM=AC+CM=3+4.5=7.5cm

Given that the line AB = 6, the point C is on the line AB, and BC = 2, the point m is the midpoint of the line AC, the length of the line BM can be obtained

AB=6
BC=2
So AC = ab-bc = 6-2 = 4
Because m is the midpoint of AC, BM = 1 / 2 * AC = 2
So BM = BC + BM = 2 + 2 = 4

Given the line segment AB = 20cm, take point C on the extension line of line segment AB so that BC = half AB, and point m is the midpoint of line segment AC, then the length of line segment BM is

A————M——B——C
∵BC＝AB/2＝20/2＝10
∴AC＝AB+BC＝20+10＝30
∵ m is the midpoint of AC
∴AM＝AC/2＝30/2＝15
∴BM＝AB-AM＝20-15＝5（cm）