Question

Line segment of length k is divided into 3 equal parts. What is distance between midpoints of first and third segments?

Answer 1

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

Answer 2

k is divided into 3 equal parts: 0 to k/3, k/3 to 2k/3 and 2k/3 to k.

midpoint of first segment = (0+k/3)/2 = k/6

midpoint of third segment = (2k/3+k)/2 = 5k/6

distance in between = 5k/6-k/6 = 2k/3

The answer is A).