Question

Find the centroid of the triangle whose vertices are (4,-8) (-9,7) and (8,13)

Answer 1

Step-by-step explanation:

Centroid formula=(x1+x2+x3/3, y1+y2+y3/3)

=4-9+8/3,-8+7+13/3

=(1,4)

Answer 2

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

$\green{\therefore{\text{Centroid(G)=}(1,4)}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Coordinate \: of \: A = (4,-8)} \\ \\ : \implies \text{Coordinate \: of \: B = (-9,7)} \\ \\ : \implies \text{Coordinate \: of \: C = (8,13)} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Centroid(G) = ?}$

• According to given question :

$\bold{As \: we \: know \: that} \\ \circ \: \text{Centroid \: of \: triangle(G}) \\ \\ \circ \: \text{For \: x }= \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ \circ \: \text{For \: y} = \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ \text{Let \: Coordinate \: of \: (g) =( x,y) } \\ \\ \bold{For \: x}\\ : \implies x = \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ : \implies x = \frac{ 4 +(-9)+ 8}{3} \\ \\ : \implies x = \frac{12-9}{3} \\ \\ \green{: \implies x =1}\\ \\ \bold{For \: y}\\ : \implies y= \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ : \implies y= \frac{(-8 ) +7+13}{3} \\ \\ : \implies y = \frac{20-8}{3} \\ \\ \green{: \implies y =4} \\ \\ \green{\therefore \text{Coordinate \: of \: centroid(G) = }(1,4)}$