In triangle ∆pqr, c is the centroid.
a. if cy = 10, find pc and py
b. if qc = 10, find zc and zq
c. if px = 20, find pq

Refer to the redrawn figure below.

Because C is the centroid, 
PZ = ZR;  QY = YR; and PX = XQ.

Part a.
If CY = 10, then PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30

PC = 20
PY = 30

Part b.
If QC = 10, then ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15

ZC = 5
ZQ = 15

Part c.
Given: PX = 20.
Because the median bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40

PQ = 40