Question

Find the coordinates of centroid of the following:i. (-1, 3), (6, -3) and (-3, 6) ii. (6, 2), (0, 0) and (4, -7)iii. (1, -1), (0, 6) and (-3, 0)

Answer 1

In the attachments I have answered this problem.   I have applied the formula to find  centroid of the triangle formed by the  given points .    See the attachment for detailed solution.

Answer 2

if vertices of triangle are $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3)$ are given then,
centroid is $\{\frac{(x_1+x_2+x_3)}{3},\frac{(y_1+y_2+y_3)}{3}\}$

i. (-1, 3) , (6 -3) and (-3, 6)
so, centroid = {(-1 + 6 -3)/3 , (3 - 3 + 6)/3}
= (2/3 , 2)

ii. (6,2) , (0,0) and (4, -7)
so, centroid = {(6 + 0 + 4)/3, (2 + 0 -7)/2}
=(10/3 , -5/2)

iii. (1,-1) , (0,6) and (-3,0)
so, centroid = {(1 + 0 - 3)/3 , (-1 + 6 + 0)/3}
= (-2/3 , 5/3)