Question

Find the centroid of the triangle whose vertices are (7,5), (5,7) and (-3,3).

Answer 1

SOLUTION

REFER TO ATTACHMENT

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Answer 2

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

$\green{\therefore{\text{Centroid(G)=}(3,5)}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Coordinate \: of \: A = (7,5)} \\ \\ : \implies \text{Coordinate \: of \: B = (5,7)} \\ \\ : \implies \text{Coordinate \: of \: C = (-3,3)} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Centroid(G) = ?}$

• According to given question :

$\bold{As \: we \: know \: that} \\ \circ \: \text{Centroid \: of \: triangle(G}) \\ \\ \circ \: \text{For \: x }= \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ \circ \: \text{For \: y} = \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ \text{Let \: Coordinate \: of \: (g) =( x,y) } \\ \\ \bold{For \: x}\\ : \implies x = \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ : \implies x = \frac{7+5+ (-3)}{3} \\ \\ : \implies x = \frac{9}{3} \\ \\ \green{: \implies x =3} \\ \\ \bold{For \: y}\\ : \implies y= \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ : \implies y= \frac{5+7+3}{3} \\ \\ : \implies y = \frac{15}{3} \\ \\ \green{: \implies y =5} \\ \\ \green{\therefore \text{Coordinate \: of \: centroid(G) = }(3,5)}$