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)

$-2, - \frac {16}{3}, 2$

Answer 2

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 $c = 2$
$\therefore \left( a, b, c\right)\equiv \left(-2, -\frac{16}{3}, 2\right)$