Question

If the centroid of $△ABC$ whose vertices are $A(-3,2)$ and $B(-2,1),$ lies on the line $3x+4y+2=0$, then the locus of vertex $C$ is

• A. $4x+3y+5=0$
• B. $3x+4y+3=0$
• C. $4x+3y+3=0$
• D. $3x+4y+5=0$

Answer 1

The correct option is B $3x+4y+3=0$

Let $C\equiv (h,k)$
$\Rightarrow \text{Centroid}G\equiv (\frac{h-5}{3},\frac{k+3}{3})$


$\because G$ lies on line $3x+4y+2=0$
$\therefore 3\left(\frac{h-5}{3}\right)+4\left(\frac{k+3}{3}\right)+2=0$
$\Rightarrow 3(h-5)+4(k+3)+6=0$
Hence, the locus of $C(h,k)$ is $3x+4y+3=0.$