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  4. 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

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Q. 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

COMEDKCOMEDK 2015Straight Lines

Solution:

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

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$\therefore \:\: G \left( \frac{ 0 + a + 0}{3} , \frac{0 +0 +b}{3} \right) = (1,2)$ (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$