Question

Find the Centroid of the triangle whose vertices are x(2,8),y(-2,2)&z(6,-4).​

Answer 1

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

$\sf \: Coordinates \: of \: the \: vertices \: are: \: x(2,8), \: y(-2,2) \: and \: z(6,-4)$

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

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

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

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

$\sf \: x(2,8) \: \rightarrow \: (x_{1}, y_{1}) \\ \\\sf \: y(-2,2) \: \rightarrow \: (x_{2}, y_{2}) \\ \\ \sf \: z(6,-4) \: \rightarrow \: (x_{3}, y_{3})$

$\large{\pink{\bold{\underline{Now:}}}} \\ \\ \rightarrow \: \sf \: Centroid = ( \frac{2 + ( - 2) + 6}{3}) ,( \frac{8 + 2 + (-4)}{3} ) \\ \\ \rightarrow \sf \: Centroid = ( \frac{2 - 2 + 6}{3}) , (\frac{8 + 2 - 4}{3} ) \\ \\ \rightarrow \sf \: Centroid = ( \frac{6}{3} ),( \frac{10 - 4}{3} ) \\ \\ \rightarrow \sf \: Centroid = ( \frac{\cancel6}{\cancel3} ),( \frac{\cancel6}{\cancel3} ) \\ \\ \rightarrow \sf \: Centroid = (2,2)$

$\large{\orange{\bold{\underline{Therefore:}}}} \\ \\ \sf \: The \: coordinates \: of \: Centroid \: of \: the \: triangle \\ \sf \: is \: (2,2 ).$