A straight lines meets the coordinates axes at $A$ and $B$, so that the centroid of the $\triangle O A B$ is $(1,2)$. Then, the equation of the line $A B$ is

• A

  $x+y=6$
• Correct answer
  B

  $2 x+y=6$
• C

  $x+2 y=6$
• D

  $3 x+y=6$

Solution

Since, straight line meets the coordinate axes at $A$ and $B$, so equation of line intercept form is $\frac{x}{a}+\frac{y}{b}=1$. Let $G$ represents the centroid of $\triangle O A B$. Given that $G=(1,2)$.

$\therefore$ Centroid $G\left(\frac{0+a+0}{3}, \frac{0+0+b}{3}\right)=(1,2) \quad$ (given) $\Rightarrow \frac{a}{3}=1 \Rightarrow a=3, \frac{b}{3}=2 \Rightarrow b=6$ Hence, required equation of line is $$ \frac{x}{3}+\frac{y}{6}=1 \Rightarrow 2 u+i j=6 $$

Hence, the correct answer is option: 'B'.