Question

Find the centroid of the triangle whose vertices are (5,1),(3,-4)and (1,8)

Answer 1

5+3+1÷3=3

1-4+8÷3=5/3

then centroid is (3, 5/3)

Answer 2

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

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

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Coordinate \: of \: A = (5,1)} \\ \\ : \implies \text{Coordinate \: of \: B = (3,-4)} \\ \\ : \implies \text{Coordinate \: of \: C = (1,8)} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Centroid(G) = ?}$

• According to given question :

$\bold{As \: we \: know \: that} \\ \circ \: \text{Centroid \: of \: triangle(G}) \\ \\ \circ \: \text{For \: x }= \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ \circ \: \text{For \: y} = \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ \text{Let \: Coordinate \: of \: (g) =( x,y) } \\ \\ \bold{For \: x}\\ : \implies x = \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ : \implies x = \frac{ 5 +3 + 1}{3} \\ \\ : \implies x = \frac{9}{3} \\ \\ \green{: \implies x =3} \\ \\ \bold{For \: y}\\ : \implies y= \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ : \implies y= \frac{ 1 +(-4)+8}{3} \\ \\ : \implies y = \frac{9-4}{3} \\ \\ \green{: \implies y =\frac{5}{3}} \\ \\ \green{\therefore \text{Coordinate \: of \: centroid(G) = }(3,\frac{5}{3})}$