Fill in the blanks.

Point G is the centroid of ∆ABC.

(1) If l(RG) = 2.5 then l(GC) = ......

(2) If l(BG) = 6 then l(BQ) = ......

(3) If l(AP) = 6 then l(AG) = ..... and l(GP) = .....

1) If then, as we know that the centroid divides each median in the ratio 2:1.

Hence,

GC/2.5 = 2/1

Cross Multiplying we get,

GC × 1 = 2 × 2.5

Therefore, I(GC) = 5

2) If then , as we know that the centroid divides each median in the ratio 2:1.

Now,

6/QG = 2/1

6 × 1 = 2 × QG

6 = 2 × QG

6/2 = QG

Hence, I(QG) = 3.

Since we have to find I(BQ), and from the figure it can be seen that,

(BQ) = I(BG) + I(QG)

Therefore, I(BQ) = 6 + 3

I(BQ) = 9.

3) If then and l(GP) = 2, as we know that the centroid divides each median in the ratio 2:1 --------(i)

Here both I(AG) and I(GP) are unknown so,

Let I(AG), I(GP) be 2x and x respectively, from equation (i)

Since, I(AP) = I(AG) + I(GP)

6 = 2x + x

6 = 3x

6/3 = x

x = 2.

Therefore, I(AG) = 2x = 2×2 = 4.

I(GP) = x = 2.