Line segment of length k is divided into 3 equal parts.
so first segment is 0-k/3 and third segment is 2/3k-k
so mid-pt of 1st = k/6 and 3rd = 5/6k
so the distance in between = 5/6k-k/6 = 4/6k = 2/3k
ans is A
The distance between the midpoints of the first segment and the third segment is 2k/3. Hence, option A is the right choice.
The mid-point of a line segment is the point from which the distance to both ends of the line segment is equal.
In the question, we are given a line segment of length k units, which is divided into 3 equal parts.
We are asked to find the distance between the midpoints of the first and third segments.
Firstly, we divide the line segment at points k/3 and 2k/3, to get three equal parts of lengths k/3 each.
Now, the mid-point of the first segment = (0 + k/3)/2 = k/6.
The mid-point of the third segment = (2k/3 + k)/2 = 5k/6
Therefore, the distance between the midpoints of the first segment and the third segment is (5k/6 - k/6) = 4k/6 = 2k/3. Hence, option A is the right choice.
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