Question

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

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

Answer 1

Answer: (A)

$2x+3y=9$

Let $C$ be $(h,k)$

$\therefore$ centroid is $(\frac{h}{3},\frac{k-2}{3}).$ As it lies on $2x+3y=1$

$\therefore \frac{2h}{3}+(k-2)=1\Rightarrow$ locus is $2x+3y=9.$