Answer:
[tex]C = (\frac{11}{3},\frac{11}{3},\frac{7}{3})[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1,z_1) = (1,3,-2)[/tex]
[tex](x_2,y_2,z_2) = (4,5,0)[/tex]
[tex](x_3,y_3,z_3) = (6,3,9)[/tex]
Required
Determine the coordinates of the centroid
Represent the coordinates with C.
C is calculated as follows:
[tex]C = (\frac{1}{3}(x_1+x_2+x_3),\frac{1}{3}(y_1+y_2+y_3),\frac{1}{3}(z_1+z_2+z_3}))[/tex]
Substitute values of x and y in the given equation
[tex]C = (\frac{1}{3}(1+4+6),\frac{1}{3}(3+5+3),\frac{1}{3}(-2+0+9}))[/tex]
[tex]C = (\frac{1}{3}(11),\frac{1}{3}(11),\frac{1}{3}(7}))[/tex]
[tex]C = (\frac{11}{3},\frac{11}{3},\frac{7}{3})[/tex]
The above is the coordinate of the centroid
