Question

The coordinate of centroid of a triangle whose vertices are (1,3,-2), (4,5,0), (6,3,9) is = ……………….

Answer 1

`C = ((11)/(3),(11)/(3),(7)/(3))`

Explanation:

Given

`(x_1,y_1,z_1) = (1,3,-2)`

`(x_2,y_2,z_2) = (4,5,0)`

`(x_3,y_3,z_3) = (6,3,9)`

Required

Determine the coordinates of the centroid

Represent the coordinates with C.

C is calculated as follows:

`C = ((1)/(3)(x_1+x_2+x_3),(1)/(3)(y_1+y_2+y_3),(1)/(3)(z_1+z_2+z_3}))`

Substitute values of x and y in the given equation

`C = ((1)/(3)(1+4+6),(1)/(3)(3+5+3),(1)/(3)(-2+0+9}))`

`C = ((1)/(3)(11),(1)/(3)(11),(1)/(3)(7}))`

`C = ((11)/(3),(11)/(3),(7)/(3))`

The above is the coordinate of the centroid