Question

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

Answer 1

C =[(x1+x2+x3) /3, (y1+y2+y3) /3]

=[(4+8-9)/3, (-8+13+7)/3)]

=[(3/3), (12/3)]

=[1,4]

Hope this helps... ☺

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 :

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