Question

find the centroid of the triangle whose vertices are(1,4)(-1,1)(3,-2)
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Answer 1

Answer:

-5/2,-7/3

Step-by-step explanation:

• x1+x2+x2/3 , y1+y2+y3/3
• 1+(-1)+3/3 , 4+1+(-2)/3
• -5/3 , -7/3

Answer 2

Step-by-step explanation:

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

$\sf \: Coordinates \: of \: the \: vertices \: are: \: x(1,4), \: y(-1,1) \: and \: z(3,-2)$

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

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

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

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

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

$\large{\pink{\bold{\underline{Now:}}}} \\ \\ \rightarrow \: \sf \: Centroid = ( \frac{1 + ( - 1) + 3}{3}) ,( \frac{4 + 1 - 2}{3} ) \\ \\ \rightarrow \sf \: Centroid = ( \frac{0 + 3}{3}) , (\frac{5 - 2}{3} ) \\ \\ \rightarrow \sf \: Centroid = ( \frac{3}{3} ),( \frac{3}{3} ) \\ \\ \rightarrow \sf \: Centroid = (1,1)$

$\large{\orange{\bold{\underline{Therefore:}}}} \\ \\ \sf \: The \: coordinates \: of \: Centroid \: of \: the \: triangle \\ \sf \: is \: (1,1).$