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If the centroid of a triangle formed by $(7, x),(y,-6)$ and (9,10) is $(6,3)$, then the values of $x$ and $y$ are respectively
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The correct answer is:
5,2
Centroid of given triangle $=\left(\frac{7+\mathrm{y}+9}{3}, \frac{\mathrm{x}-6+10}{3}\right)$
$\Rightarrow\left(\frac{16+\mathrm{y}}{3}, \frac{\mathrm{x}+4}{3}\right)=(6,3)$
$\Rightarrow 16+\mathrm{y}=18 ; \mathrm{x}+4=9$
$\Rightarrow \mathrm{y}=2 ; \mathrm{x}=5$
$\Rightarrow\left(\frac{16+\mathrm{y}}{3}, \frac{\mathrm{x}+4}{3}\right)=(6,3)$
$\Rightarrow 16+\mathrm{y}=18 ; \mathrm{x}+4=9$
$\Rightarrow \mathrm{y}=2 ; \mathrm{x}=5$
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