## The length of a line segment is m. This segment is divided into: a) three equal parts; b) five equal parts. Find the distance between the mi

Question

The length of a line segment is m. This segment is divided into: a) three equal parts; b) five equal parts. Find the distance between the midpoints of the first and the last parts in each case.

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2m/3 and 2m/5

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• a) 2/3·m
• b) 4/5·m

### Explanation:

Consider the case where each part is of length 1. Then the midpoint of the first segment is at 1/2.

a) If there are 3 segments, the midpoint of the last segment is halfway between 2 and 3, at 2 1/2. The distance from the first midpoint to the last midpoint is …

… 2 1/2 – 1/2 = 2 . . . . . that is, 2/3 of the total line length

When the line length is m, that is 2/3·m

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b) If there are 5 segments, the midpoint of the last segment is halfway between 4 and 5, at 4 1/2. The distance from the first midpoint to the last midpoint is …

… 4 1/2 – 1/2 = 4 . . . . . that is, 4/5 of the total line length

When the line length is m, that is 4/5·m