Final answer:
In triangle ARP, the centroid E is on the median AX. By setting AE = EX and solving for y, we can determine the value of AE. Then, by multiplying AE by 2, we can find the value of AC.
Step-by-step explanation:
In triangle ARP, the centroid E is on the median AX, which means that E divides AX into two equal parts. Therefore, AE = EX.
Given that AE = 6y and EX = 3y - 2, we can equate the two expressions:
6y = 3y - 2
Subtracting 3y from both sides:
3y = -2
Dividing by 3 on both sides:
y = -2/3
Substituting this value of y back into AE:
AE = 6(-2/3) = -4
Since AC is a median, it is also divided into two equal parts by the centroid E. Therefore, AC = 2 * AE = 2 * (-4) = -8.