Question

what is the length of segment ns?
1 unit
2 units
4 units
6 units

Explanation:

Step1: Use the property of the centroid

In a triangle, the centroid divides each median in a ratio of \(2:1\). Here, \(NS\) and \(SR\) are parts of the median \(NR\) such that \(NS = 7x - 3\) and \(SR=5x - 3\). Also, since the centroid divides the median, \(NS = 2\times SR\).
So, \(7x - 3=2\times(5x - 3)\).

Step2: Solve the equation for \(x\)

Expand the right - hand side: \(7x - 3 = 10x-6\).
Move the \(x\) terms to one side and constants to the other side: \(6 - 3=10x - 7x\).
Simplify: \(3 = 3x\), then \(x = 1\).

Step3: Calculate the length of \(NS\)

Substitute \(x = 1\) into the expression for \(NS\): \(NS=7x - 3\).
\(NS=7\times1 - 3=4\).

Answer:

4 units