Question

Find the centroid of triangle whose vertices are (1,3) (-2,7) (5,-3)

Answer 1

Here is the answer of your question.
Hope this will help you

Answer 2

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

$\green{\therefore{\text{Centroid(G)}=(\frac{4}{3},\frac{7}{3})}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Coordinate \: of \: A = (1,3)} \\ \\ : \implies \text{Coordinate \: of \: B = (-2,7)} \\ \\ : \implies \text{Coordinate \: of \: C = (5,-3)} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies Centroid(G) = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \circ \: \text{Centroid \: of \: triangle(G}) \\ \\ \circ \: \text{For \: x }= \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ \circ \: \text{For \: y} = \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ \text{Let \: Coordinate \: of \: (g) =( x,y) } \\ \\ \bold{For \: x}\\ : \implies x = \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ : \implies x = \frac{ 1 +(-2 )+ 5}{3} \\ \\ : \implies x = \frac{1-2+5}{3} \\ \\ \green{: \implies x =\frac{4}{3}} \\ \\ \bold{For \: y}\\ : \implies y= \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ : \implies y= \frac{ 3 + 7+ (-3)}{3} \\ \\ : \implies y = \frac{10-3}{3} \\ \\ \green{: \implies y =\frac{7}{3}} \\ \\ \green{\therefore \text{Coordinate \: of \: centroid(G) }= (\frac{4}{3},\frac{7}{3})}$