In triangle ARP, centroid E is on median AX. AE = y+6 and EX = 3y-2. Find AX
A 7/3
B 13
C 5 1/2
D 11
We know that the centroid divides the median into two segments, and the ratio of the lengths of the smaller and larger segment is 2:1.
Let's suppose that AE = 2x and EX = x.
According to the problem statement, AE = y + 6 and EX = 3y - 2.
So, we have 2x = y + 6 and x = 3y - 2.
Now, we can solve this system of equations to find the values of x and y.
From the first equation, we can express y in terms of x:
2x = y + 6
y = 2x - 6
Substituting this value into the second equation, we get:
x = 3(2x - 6) - 2
x = 6x - 18 - 2
x - 6x = -20
-5x = -20
x = 4
Now, we can find y:
y = 2x - 6
y = 2(4) - 6
y = 2
Since AE = 2x and EX = x, we have AE = 2(4) = 8 and EX = 4.
Finally, we can find AX:
AX = AE + EX
AX = 8 + 4
AX = 12.
Therefore, the answer is AX = 12.
(Sidenote: The answer choices provided do not match the calculated result. Please double-check the options)