Question

Z is centroid of triangle RST. What is RW, if RV=4x+3, WS=5x-1, and VT=2x+9?

Answer 1

Part (a):
We are given that Z is the centroid of triangle RST. This means that Z is the point of intersection of the three medians of the triangle.
In other words:
W is the midpoint of RS
V is the midpoint of RT
We are given that:
RV = 4x + 3 and VT = 2x + 9
Since V is the midpoint, then:
RV = VT
4x + 3 = 2x + 9
4x - 2x = 9 - 3
2x = 6
x = 3

Part (b):
We are given that:
WS = 5x-1
x = 3
Therefore:
WS = 5(3) - 1 
WS = 15 - 1 = 14

Part (c):
Since W is the midpoint of RS, therefore RW = WS
We calculated WS = 14
Therefore:
RW = 14