Question

Find the centroid of the triangle whose vertices are (2,4) (6,4) (2,0)​

Answer 1

Answer:

G(x,y) = (10/3, 8/3).

Step-by-step explanation:

centroid G(x,y) =

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

= ((2+6+2)/3, (4+4+0)/3)

G(x,y) = (10/3, 8/3).

Answer 2

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

$\green{\therefore{\text{Centroid(G)=}(\frac{10}{3},\frac{8}{3})}}$

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

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

• According to given question :

$\bold{As \: we \: know \: that} \\ \circ \: \text{Centroid \: of \: triangle(G}) \\ \\ \circ \: \text{For \: x }= \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ \circ \: \text{For \: y} = \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ \text{Let \: Coordinate \: of \: (g) =( x,y) } \\ \\ \bold{For \: x}\\ : \implies x = \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ : \implies x = \frac{ 2 +6 + 2}{3} \\ \\ : \implies x = \frac{10}{3} \\ \\ \green{: \implies x =\frac{10}{3}} \\ \\ \bold{For \: y}\\ : \implies y= \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ : \implies y= \frac{ 4+4+0}{3} \\ \\ : \implies y = \frac{8+0}{3} \\ \\ \green{: \implies y =\frac{8}{3}} \\ \\ \green{\therefore \text{Coordinate \: of \: centroid(G) = }(\frac{10}{3},\frac{8}{3})}$