Question

If origin is the centroid of a $\Delta PQR$ with vertices $P(2a,2,6),Q(-4,3b,-10)$ and $(8,14,2c)$ , then the value of $a,b$ and $c$ are respectively.

• A. $-2,2,2$
• B. $-2,2,-\frac{16}{3}$
• C. $-2,-\frac{16}{3},2$
• D. $-\frac{16}{3},-2,2$

Answer 1

Answer: (C)

Coordinates of centroid of $\Delta PQR$
$\equiv \left(\frac{2a-4+8}{3},\frac{2+3b+14}{3},\frac{6-10+2c}{3}\right)$
But it is given that origin is the centroid of $\Delta PQR$
$\therefore \left(0,0,0\right)=\left(\frac{2a+4}{3},\frac{3b+16}{3},\frac{2c-4}{3}\right)$
On comparing both sides, we get
$\frac{2a+4}{3}=0,\frac{3b+16}{3}=0$ and $\frac{2c-4}{3}=0$
$\Rightarrow 2a=-4,3b=-16$ and $2c=4$
$\Rightarrow a=-2,b=-\frac{16}{3}$ and $c=2$
$\therefore \left(a,b,c\right)\equiv \left(-2,-\frac{16}{3},2\right)$