Question

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

• A. $x + y = 6$
• B. $2x + y = 6$
• C. $x +2y = 6$
• D. $3x + y = 6$

Answer 1

Answer: (B)

$2x + y = 6$

Answer 2

Since straight line meets the coordinate axes at A and B, so equation of line in intercept from is $\frac{x}{a} + \frac{y}{b} = 1$

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