Question

find the coordinates of centroid of a triangle whose vertices are (2,6)(8,12)(8,3)
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Answer 1

$\bold\red{\underline{\underline{Answer:}}}$

$\bold{Coordinates \ of \ centroid \ of \ triangle}$

$\bold{are \ (6,7)}$

$\bold\blue{Explanation}$

$\bold{Coordinates \ of \ centroid }$

$\bold{=(\frac{x1+x2+x3}{3}),(\frac{y1+y2+y3}{3})}$

$\bold\orange{Given:}$

$\bold{Vertices \ are:}$

$\bold{=>(x1,y1)=(2,6)}$

$\bold{=>(x2,y2)=(8,12)}$

$\bold{=>(x3,y3)=(8,3)}$

$\bold\pink{To \ find:}$

$\bold{Coordinates \ of \ centroid \ of \ triangle}$

$\bold\green{\underline{\underline{Solution}}}$

$\bold{By \ centroid \ formula}$

$\bold{Coordinates \ of \ centroid}$

$\bold{=(\frac{x1+x2+x3}{3}),(\frac{y1+y2+y3}{3})}$

$\bold{=\frac{2+8+8}{3},\frac{6+12+3}{3}}$

$\bold{=\frac{18}{3},\frac{21}{3}}$

$\bold{=6,7}$

$\bold\purple{\tt{\therefore{Coordinates \ of \ centroid \ of \ triangle}}}$

$\bold\purple{are \ (6,7)}$

Answer 2

$\red{\bold{\underline{\underline{Answer}}}}$

$\tt\green{\therefore{Centroid=(6,7)}}$

$\pink{\bold{\underline{Step-by-step\:explanation}}}$

• Given

$\tt \implies Coordinate \: of \: p = (2,6) \\ \\ \tt \implies Coordinate \: of \: q= (8,12) \\ \\ \tt \implies Coordinate \: of \: r= (8,3)$

• To find

$\tt \implies Centroid = ?$

For finding value of centroid :

$\tt \implies x = \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ \tt \implies x = \frac{2+8+8}{3} \\ \\ \tt \implies x = 6 \\ \\ \tt \implies y=\frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\\tt \implies y= \frac{6 + 12+3}{3} \\ \\ \tt \implies y= 7 \\ \\ \green{\tt \therefore Centroid \: is \: (6,7)}$