Find the $3^{t h}$ vertex of Triangle whose vertices are $A (- 5, 7), B (- 4, - 5), C (x, y)$ and circumcenter is origin

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Solution

$A (- 5, 7), B (- 4, - 5), C (x, y)$
Circumcenter is given by $(\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3}) (\frac{- 5 - 4 + x}{3}, \frac{7 - 5 + y}{3}) = (0, 0) x - 9 = 0; y + 2 = 0 x = 9, y = - 2$
The $3 r d$ vertex is $(9, - 2)$

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