MathematicsA line meets the coordinate axes at A and B such that the centroide of The equation of the line AB is

A line meets the coordinate axes at A and B such that the centroide of The equation of the line AB is

A
x+y=6
B
2x+y=6
C
x+2y=6
D
x+y=8

Solution:

$\begin{array}{l} L e t A (a, 0), B (0, b) a n d O (0, 0) \\ G = (\frac{a + 0 + 0}{3}, \frac{0 + b + 0}{3}) \\ \Rightarrow (1, 2) = (\frac{a}{3}, \frac{b}{3}) \\ \frac{a}{3} = 1, \frac{b}{3} = 2 \\ a = 3, b = 6 \\ E q u a t i o n o f \bar{A B} i s \frac{x}{a} + \frac{y}{b} = 1 \\ \Rightarrow \frac{x}{3} + \frac{y}{b} = 1 \\ \Rightarrow 2 x + y = 6 \end{array}$

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