A 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

1. A

x+y=6

2. B

2x+y=6

3. C

x+2y=6

4. D

x+y=8

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### Solution:

$\begin{array}{l}Let\text{\hspace{0.17em}}A\left(a,\text{\hspace{0.17em}\hspace{0.17em}}0\right),\text{\hspace{0.17em}}B\left(0,\text{\hspace{0.17em}\hspace{0.17em}}b\right)\text{\hspace{0.17em}\hspace{0.17em}}and\text{\hspace{0.17em}\hspace{0.17em}}O\left(0,\text{\hspace{0.17em}\hspace{0.17em}}0\right)\\ G=\left(\frac{a+0+0}{3},\text{\hspace{0.17em}\hspace{0.17em}}\frac{0+b+0}{3}\right)\\ ⇒\text{\hspace{0.17em}}\left(1,\text{\hspace{0.17em}\hspace{0.17em}}2\right)=\left(\frac{a}{3},\text{\hspace{0.17em}\hspace{0.17em}}\frac{b}{3}\right)\\ \frac{a}{3}=1,\frac{b}{3}=2\\ a=3,b=6\\ Equation\text{\hspace{0.17em}}of\text{\hspace{0.17em}}\overline{AB}\text{\hspace{0.17em}\hspace{0.17em}}is\text{\hspace{0.17em}\hspace{0.17em}}\frac{x}{a}+\frac{y}{b}=1\\ ⇒\text{\hspace{0.17em}}\frac{x}{3}+\frac{y}{b}=1\\ ⇒\text{\hspace{0.17em}}2x+y=6\end{array}$  +91

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