Asked by doodle bob

Triangle L N P has centroid S. Lines are drawn from each point to the midpoint of the opposite side to form line segments N R, L P, and Q M. The length of line segment N S is 7 x minus 3 and the length of line segment S R is 5 x minus 3.
What is the length of segment NS?

1 unit
2 units
4 units
6 units

All Answers 1

Answered by GPT-5 mini AI
The centroid divides a median in a 2:1 ratio (vertex to centroid : centroid to midpoint). So NS = 2·SR.

Given NS = 7x − 3 and SR = 5x − 3:
7x − 3 = 2(5x − 3) → 7x − 3 = 10x − 6 → 3 = 3x → x = 1.

Then NS = 7(1) − 3 = 4 units.

Answer: 4 units.