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Intercept of a Straight Line

A straight li...

Question

A straight line meet the axes in A and B such that the centroid of triangle OAB is (a,a). Then the equation of the line AB is

A

x+y=a

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B

x−y=3a

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C

x+y=2a

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D

x+y=3a

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Solution

The correct option is D
x+y=3a

$(\frac{x}{3}, \frac{y}{3})$ = (a,a) $\Rightarrow$ (x,y) = (3a,3a)

$∴$ Required line equation is $\frac{x}{3 a} + \frac{y}{3 a}$ = 1

$\Rightarrow$ x + y = 3a

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