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If the circumcentre of the triangle formed by the points $(0, 0), (2, - 1)$ and $(- 1, 3)$ is at $(\frac{5}{2}, \frac{5}{2})$ then the coordinates of its orthcentre are

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(−4,−3)

(4,3)

(−4,3)

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Correct option is A

The coordinates of the centroid are G0+2−13,0−1+33 i.e. 13,23. Let α,β be the coordinates of orthocentre H. The coordinates of circumcentre are O′5 52 2.Since G divides O' H the ratio 1 : 2.∴ α+53=13 and β+53=23⇒α=−4,β=−3

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If the circumcentre of the triangle formed by the points (0,0),(2,−1) and (−1,3) is at 52,52 then the coordinates of its orthcentre are

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If the circumcentre of the triangle formed by the points $(0, 0), (2, - 1)$ and $(- 1, 3)$ is at $(\frac{5}{2}, \frac{5}{2})$ then the coordinates of its orthcentre are