Question

Let $A(2,-3)$ and $B(-2,1)$ be vertices of triangle ABC. if the centroid of this triangle moves on the line $2x+3y=1$. then the locus of vertex C is the line

• A. $2x+3y=9$
• B. $2x-3y=7$
• C. $3x+2y=5$
• D. $3x-2y=3$

Answer 1

The correct option is A $2x+3y=9$

Let the coordinates of C be $(h,k)$
Coordinates of centroid of triangle ABC is $(\frac{h}{3},\frac{-2+k}{3})$
Since, centroid lies on the line $2x+3y=1$
$\Rightarrow 2\left(\frac{h}{3}\right)+3\left(\frac{-2+k}{3}\right)=1$
$\Rightarrow 2h+3k=9$
$\Rightarrow 2x+3y=9$