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The Centroid

In ABC, if ...

Question

In $△ A B C$ , if the orthocenter is $(1, 2)$ and the circumceter is $(0, 0)$ , then centroid of $△ A B C$ is

(1 / 2, 2 / 3)

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(1 / 3, 2 / 3)

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(2 / 3, 1)

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N o n e o f t h e s e

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Solution

The correct option is B $(1 / 2, 2 / 3)$
The centroid divide line joining orthocentre and circumcentre in ratio 2:1
$\begin{matrix} x = \frac{1 \times 1 + 2 \times 0}{1 + 2} = \frac{1}{3} y = \frac{1 \times 2 + 2 \times 0}{1 + 2} = \frac{2}{3} \end{matrix}$

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