Question

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

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

Answer 1

Answer: (B)

Let coordinate of third vertex be $C(x_1,y_1)$ Then, centroid of triangle
$=\left(\frac{2+(-2)+x_1}{3},\frac{-3+1+y_1}{3}\right)=\left(\frac{x_1}{3},\frac{y_1-2}{3}\right)$ Since, centroid of this triangle moves on the line $2x+3y=1$
$\therefore$ $2\left(\frac{x_1}{3}\right)+3\left(\frac{y_1-2}{3}\right)=1$
$\Rightarrow$ $2x_1+3y_1-6=3$
$\Rightarrow$ $2x_1+3y_1=9$
Hence, the locus of the vertex C is the line $2x+3y=9$