Question

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Answer 1

$\large{\red{\bold{\underline{Given:}}}}$

$\sf \: Coordinates \: of \: the \: vertices \: are: \: x(6,3), \: y(9,4) \: and \: z(5,7)$

$\large{\green{\bold{\underline{To \: Find:}}}}$

$\sf \: Centroid \: of \: the \: triangle$

$\large{\blue{\bold{\underline{Formula \: Used:}}}} \\ \\ \sf \:Coordinates \: of \:Centroid = \: (\frac{x_{1} + x_{2} + x_{3}}{3} ),( \frac{y_{1} + y_{2} + y_{3}}{3})$

$\large{\red{\bold{\underline{Solution:}}}} \\ \\ \: \sf \: On \: considering \: the \: respective \: coordinates \: as :$

$\sf \: x(6,3) \: \rightarrow \: (x_{1}, y_{1}) \\ \\\sf \: y(9,4) \: \rightarrow \: (x_{2}, y_{2}) \\ \\ \sf \: z(5,7) \: \rightarrow \: (x_{3}, y_{3})$

$\large{\pink{\bold{\underline{Now:}}}} \\ \\ \rightarrow \: \sf \: Centroid = ( \frac{6 + 9 + 5}{3}) ,( \frac{3 + 4 + 7}{3} ) \\ \\ \rightarrow \sf \: Centroid = ( \frac{20}{3}) , (\frac{14 }{3} ) \\ \\ \rightarrow \sf \: Centroid = (6.6,4.6)$

$\large{\orange{\bold{\underline{Therefore:}}}} \\ \\ \sf \: The \: coordinates \: of \: Centroid \: of \: the \: triangle \\ \sf \: is \: (6.6,4.4).$

Answer 2

Answer:

$\large{\red{\bold{\underline{Given:}}}}$

$\sf \: Coordinates \: of \: the \: vertices \: are: \: x(6,3), \: y(9,4) \: and \: z(5,7)$

$\large{\green{\bold{\underline{To \: Find:}}}}$

$\sf \: Centroid \: of \: the \: triangle$

$\large{\blue{\bold{\underline{Formula \: Used:}}}} \\ \\ \sf \:Coordinates \: of \:Centroid = \: (\frac{x_{1} + x_{2} + x_{3}}{3} ),( \frac{y_{1} + y_{2} + y_{3}}{3})$

$\large{\red{\bold{\underline{Solution:}}}} \\ \\ \: \sf \: On \: considering \: the \: respective \: coordinates \: as :$

$\sf \: x(6,3) \: \rightarrow \: (x_{1}, y_{1}) \\ \\\sf \: y(9,4) \: \rightarrow \: (x_{2}, y_{2}) \\ \\ \sf \: z(5,7) \: \rightarrow \: (x_{3}, y_{3})$

$\large{\pink{\bold{\underline{Now:}}}} \\ \\ \rightarrow \: \sf \: Centroid = ( \frac{6 + 9 + 5}{3}) ,( \frac{3 + 4 + 7}{3} ) \\ \\ \rightarrow \sf \: Centroid = ( \frac{20}{3}) , (\frac{14 }{3} ) \\ \\ \rightarrow \sf \: Centroid = (6.6,4.6)$

$\large{\orange{\bold{\underline{Therefore:}}}} \\ \\ \sf \: The \: coordinates \: of \: Centroid \: of \: the \: triangle \\ \sf \: is \: (6.6,4.4).$