Question

If the coordinates of the vertices of a triangle are(2,1) ; (3,-5) and (6,4). Find the coordinates of its Centroid

Answer 1

let (X,Y) be the centroid

$x = \frac{2 + 3 + 6}{3} \\ x = \frac{11}{3} \\y = \frac{1 - 5 + 4}{3} \\ y = 0$

(11/3,0) is the the centroid of triangle

Answer 2

$\huge{\mathcal{\underline{\purple{Solution:-}}}}$

Given vertices of coordinates of triangle are (2,1) , (3,-5) and (6,4)

Centroid (G) is given by

$\large\rm\bold{\boxed{G\:=\:(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})}}$

$\large\rm{x_1,x_2,x_3\rightarrow{X-coordinates\:of\:vertices\:of\:triangle}}$

$\large\rm{y_1,y_2,y_3\rightarrow{Y-coordinates\:of\:vertices\:of\:triangle}}$

$\large\rm{\implies{G\:=\:(\frac{2+3+6}{3},\frac{1-5+4}{3})}}$

$\large\rm{\implies{G\:=\:(\frac{11}{3},\frac{0}{3})}}$

$\large\rm{\implies{G\:=\:(\frac{11}{3},0)}}$

∴ The coordinates of centroid are (11/3,0)