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JEE MATHEMATICS MCQ: 2D GEOMETRY SYSTEM

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If H(132,112)H\left(\frac{13}{2}, \frac{11}{2}\right) is the orthocentre and P(72,52)P\left(\frac{\sqrt{7}}{2}, \frac{\sqrt{5}}{2}\right) is the circumcentre of a triangle, then coordinates of the centroid are ...... .
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Correct option: C
(13+276,11+256)\left(\frac{13+2 \sqrt{7}}{6}, \frac{11+2 \sqrt{5}}{6}\right)
Option C is correct. The centroid divides the line segment joining the circumcentre and orthocentre in the ratio 1:2. Using the section formula, the coordinates of the centroid are (13+276,11+256)\left(\frac{13+2 \sqrt{7}}{6}, \frac{11+2 \sqrt{5}}{6}\right).

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