The centroid is the point of concurrency of the medians of a triangle. Therefore, in the given diagram M is the centroid.
Using the Concurrency of Medians Theorem, we can write an equation that we can use to find the desired length, MS.
CM = 2/3CS
With the Segment Addition Postulate we can rewrite CS as the sum of the two smaller segments.
Additionally, we are given that CM= 7, which we can substitute into this new equation.
CS = CM+MS ⇒ CS = 7+MS
Next, we can substitute the above expression into the initial equation.
CM = 2/3CS ⇒ 7=2/3(7 + MS)
Let's find the desired length.
