Exercise 10 Page 312

The centroid is the point of concurrency of the medians of a triangle. In the given diagram, Y is the centroid.

Using the Concurrency of Medians Theorem, we can write an equation that we can use to find one of the desired lengths, VY. VY = 2/3VX Since we are given that VX= 9, we can solve the equation above for VY.

VY=2/3( 9)

MoveRightFacToNum

a/c* b = a* b/c

VY=18/3

CalcQuot

Calculate quotient

VY=6

With the Segment Addition Postulate, we can rewrite VX as the sum of the two smaller segments. VX = VY+ YX Since we know that VX= 9 and VY= 6, we can solve the above equation for YX. 9= 6+YX ⇒ YX=3