Question

Find the co-ordinates of centroid of a triangle whose vertices are a(3,-5) , b(-7,5 ) and c (10, -2).

Answer 1

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

$\green{\therefore{\text{Centroid(G)=}(2,\frac{-2}{3})}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Coordinate \: of \: A = (3,-5)} \\ \\ : \implies \text{Coordinate \: of \: B = (-7,5)} \\ \\ : \implies \text{Coordinate \: of \: C = (10,-2)} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Centroid(G) = ?}$

• According to given question :

$\bold{As \: we \: know \: that} \\ \circ \: \text{Centroid \: of \: triangle(G}) \\ \\ \circ \: \text{For \: x }= \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ \circ \: \text{For \: y} = \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ \text{Let \: Coordinate \: of \: (g) =( x,y) } \\ \\ \bold{For \: x}\\ : \implies x = \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ : \implies x = \frac{3+(-7) + 10}{3} \\ \\ : \implies x = \frac{6}{3} \\ \\ \green{: \implies x =2} \\ \\ \bold{For \: y}\\ : \implies y= \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ : \implies y= \frac{ -5+5+(-2)}{3} \\ \\ : \implies y = \frac{-5+5-2}{3} \\ \\ \green{: \implies y =\frac{-2}{3}} \\ \\ \green{\therefore \text{Coordinate \: of \: centroid(G) = }(2,\frac{-2}{3})}$