Question

Let $A(2,-3)$ and $B(-2,1)$ be two angular points of $△ABC.$ If the centroid of the triangle moves on the line $2x+3y=1,$ then the locus of the angular point $C$ is given by

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

Answer 1

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

Let the coordinate of the angular point $C$ be $(h,k)$
Then, coordinates of the centroid is $(\frac{2-2+h}{3},\frac{-3+1+k}{3})=(\frac{h}{3},\frac{k-2}{3})$
$\because$ Centroid lies on the line $2x+3y=1$
$\therefore 2\left(\frac{h}{3}\right)+3\left(\frac{k-2}{3}\right)=1$
$\Rightarrow 2h+3k=9$
So locus will be $2x+3y=9$