Question

Find the centroid of the triangle whose vertices (2,1) (5,2) (3,4)

Answer 1

This are the co-ordinates of centroid.

Answer 2

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

$\green{\therefore{\text{Centroid(G)=}(\frac{10}{3},\frac{7}{3})}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Coordinate \: of \: A = (2,1)} \\ \\ : \implies \text{Coordinate \: of \: B = (5,2)} \\ \\ : \implies \text{Coordinate \: of \: C = (3,4)} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Centroid(G) = ?}$

• According to given question :

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