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)

$2x + 3y = 9$

Answer 2

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 $2 x+3 y=1$
$\therefore \frac{2 \alpha}{3}+3\left(\frac{\beta-2}{3}\right)=1$
$\Rightarrow \frac{2 \alpha}{3}+\frac{3 \beta-6}{3}=1$
$\Rightarrow 2 \alpha+3 \beta-6=3$
$\Rightarrow 2 \alpha+3 \beta=9$
$\therefore$ Locus of point $C$ will be $2 x+3 y=9$