Point P is the centroid of LMN. Find PN

Answer:
PN = 14
QP = 7
Step-by-step explanation:
Extend PQ to R so that QR=PQ
MQ = QL (known, mid-point)
MPLR is parallelogram (diagonal bisect each other)
MP // RL NP/PR = NE/EL = 1/1 (E mid-point, known)
NP = PR
PQ = QR = 1/2 PR = 1/2 NP
NP = 2 PQ
NP + PQ = 2PQ + PQ = 3 PQ = QN = 21
PQ = 7
PN = 14