Question

Let $A(2,-3)$ and $B(-2,1)$ be two angular points of $\Delta ABC$. 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

Answer: (A)

Let the coordinates of $C$ be $(\alpha ,\beta )$.
$\therefore$ Coordinates of centroid
$=\left(\frac{2-2+\alpha }{3},\frac{-3+1+\beta }{3}\right)$
$=\left(\frac{\alpha }{3},\frac{\beta -2}{3}\right)$
Since, centroid lie on $2x+3y=1$
$\therefore \frac{2\alpha }{3}+3\left(\frac{\beta -2}{3}\right)=1$
$\Rightarrow \frac{2\alpha }{3}+\frac{3\beta -6}{3}=1$
$\Rightarrow 2\alpha +3\beta -6=3$
$\Rightarrow 2\alpha +3\beta =9$
$\therefore$ Locus of point $C$ will be $2x+3y=9$