Point m is located on the segment AB = 12 so that AM: MB = 1: 2. find the distance between

Point m is located on the segment AB = 12 so that AM: MB = 1: 2. find the distance between the midpoints of the segments AM and AB.

Let us denote by x the length of the segment AB, then from the proportion in the condition of the problem we can denote the length of the segment MB as 2x (since MB is twice as large as AM). Let’s compose the equation for the length of the segment AB:
x + 2x = 12.
Find x from the equation:
3x = 12;
x = 12: 3;
x = 4 – the length of the segment AM.
Let’s find the length of the MВ:
2 * 4 = 8.
Find the midpoint of the segment AM:
4: 2 = 2.
Find the midpoint of the segment AB:
12: 2 = 6.
Let’s find the distance between the midpoints of the segments AM and AB:
6 – 2 = 4.
ANSWER: 4.