Question

$A=(2,5)$ , $B=(4,-11)$ and the locus of $C$ is $9x+7y+4=0$ then the locus of the centroid of $\Delta ABC$ is

• A. $27x+21y-8=0$
• B. $3x+4y-2=0$
• C. $24x+22y-6=0$
• D. $5x+3y-7=0$

Answer 1

Answer: (A)

$27x+21y-8=0$

Given $A=(2,5),B=(4,-11)$ locus of $C$ is $9x+7y+4=0$

Let $(x_1,y_1)$ be a point on the locus of $C$ and $(h,k)$ be the centroid

we know that if $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ form a triangle the the centroid $\Rightarrow (\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

So,

$h=\frac{2+4+x_1}{3}=\frac{6+x_1}{3}$

$k=\frac{5-11+y_1}{3}=\frac{-6+y_1}{3}$

$x_1=3h-6$

$y_1=3k+6$

substitute them in the locus of $C$

$9(3h-6)+7(3k+6)+4=0$

$27h+21k-8=0$

$\therefore$ the locus of centroid is $27x+21y-8=0$