Question

find the centroid of the triangle whose vertices are (-1,4),(5,2),(-1,3)

Answer 1

let the centroid be (x,y)
so,
x = (-1+5-1)/3 = 3/3 = 1
y = (4+2+3)/3 = 9/3 = 3
so,
centroid is (1,3)

Answer 2

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

$\green{\therefore{\text{Centroid(G)=}(1,3)}}$

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

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

• According to given question :

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