If the axes are translated to the circumcentre of the triangle formed by $(9, 3), (- 1, 7), (- 1, 3)$ , then the centroid of the triangle in the new system is

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$(5, \frac{5}{3})$

(4,3)

$(\frac{- 5}{3}, \frac{- 2}{3})$

(0,0)

answer is C.

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Detailed Solution

Given points forms a right angle triangle.
circum centre = Mid point of AB = (4,5)
Centroid $G = (\frac{7}{3}, \frac{13}{3})$
$∴$ centroid in the new system $= (\frac{7}{3} - 4, \frac{13}{3} - 5) = (\frac{- 5}{3}, \frac{- 2}{3})$

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