Answer:
(2/3)m units
Step-by-step explanation:
The segment is m units long. After dividing it into 3 three equal parts, each part is m/3 units long. The midpoint of the first part is located at (m/3)/2 = m/6 units from the beginning of the segment. The midpoint of the last part is located at (2/3)m + m/6 = (5/6)m units from the beginning of the segment. Then, the distance between the midpoints of the first and the last parts is (5/6)m - m/6 = (2/3)m units
Line can be divided into segments.
The distance between the two midpoints is 2m/3
The length of the segment is given as:
[tex]\mathbf{Length = m}[/tex]
The length of each segment, after dividing them into 3 segments is:
[tex]\mathbf{Segment = \frac m3}[/tex]
The midpoint of the first segment is:
[tex]\mathbf{First= \frac m6}[/tex]
The midpoint of the third segment is the sum of the first two segments, and the half a segment
So, we have:
[tex]\mathbf{Third = \frac m3 + \frac m3 + \frac m6}[/tex]
[tex]\mathbf{Third = \frac{5m}{6}}[/tex]
So, the distance between the two midpoints is:
[tex]\mathbf{Distance = \frac{5m}{6} - \frac{m}{6}}[/tex]
[tex]\mathbf{Distance = \frac{5m - m}{6}}[/tex]
[tex]\mathbf{Distance = \frac{4 m}{6}}[/tex]
[tex]\mathbf{Distance = \frac{2m}{3}}[/tex]
Hence, the distance between the two midpoints is 2m/3
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