Question

In triangle ∆PQR, C is the centroid.

If PX = 25, find PQ



If CY = 9, find PC and PY



If QC = 12, find ZC and ZQ

not 100% sure how to figure this out

Answer 1

Given that P is the Centroid of the triangle PQR, it then follows that:
PZ = ZR ... (Equation 1)
QY = YR ... (Equation 2)
PX = XQ ... (Equation 3)

QUESTION 1
If PX = 25, find PQ
From the diagram, PQ = PX + XQ

Remember, PX = XQ ... (Equation 3)
Therefore, PQ = PX + XQ = PX + PX
⇒ PQ = PX + PX
PQ = 2(PX)

Since PX = 25
PQ - 2(25)
PQ = 50


QUESTION 2
If CY = 9, find PC and PY

We know that the centroid of a triangle divides each median into segments with a 2:1 ratio, therefore:

PC = 2(CY)
Since CY = 9,
PC = 2(9)
PC = 18

From the diagram, we see that,
PY = PC + CY
PC = 18, CY = 9
PY = 18 + 9
PY = 27


QUESTION 3
If QC = 12, find ZC and ZQ

Again, going by the fact that the centroid of a triangle divides each median into segments with a 2:1 ratio,

ZC = QC/2
Since QC = 12
ZC = 12/2
ZC = 6

From the diagram, we see that
ZQ = ZC + QC
ZC = 6, QC = 12
ZQ = 6 + 12
ZQ = 18