Question

Find the centroid of the triangle whose vertices are (6,2), (0,0) and (4, -7)

Answer 1

formula of centroid of triangle is x1+x2+x3 upon 3 and y1+y2+y3 upon 3
x=10/3
y=-5/3

Answer 2

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

$\green{\therefore{\text{Centroid(G)=}(\frac{10}{3},\frac{-5}{3})}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Coordinate \: of \: A = (6,2)} \\ \\ : \implies \text{Coordinate \: of \: B = (0,0)} \\ \\ : \implies \text{Coordinate \: of \: C = (4,-7)} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Centroid(G) = ?}$

• According to given question :

$\bold{As \: we \: know \: that} \\ \circ \: \text{Centroid \: of \: triangle(G}) \\ \\ \circ \: \text{For \: x }= \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ \circ \: \text{For \: y} = \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ \text{Let \: Coordinate \: of \: (g) =( x,y) } \\ \\ \bold{For \: x}\\ : \implies x = \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ : \implies x = \frac{ 6 + 0 + 4}{3} \\ \\ : \implies x = \frac{6+4}{3} \\ \\ \green{: \implies x =\frac{10}{3}} \\ \\ \bold{For \: y}\\ : \implies y= \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ : \implies y= \frac{ 2 +0+(-7)}{3} \\ \\ : \implies y = \frac{2-7}{3} \\ \\ \green{: \implies y =\frac{-5}{3}} \\ \\ \green{\therefore \text{Coordinate \: of \: centroid(G) = }(\frac{10}{3},\frac{-5}{3})}$