Coordinates of a centroind

Let’s A = [3, 2, 0], B = [1, -2, 4] and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians).

Correct result:

x =  1.6667
y =  0.3333
z =  1.6667

Solution:

$$\begin{gathered} x_0=3 \\ {y}_0=2 \\ {z}_0=0 \\ {x}_1=1 \\ {y}_1=-2 \\ {z}_1=4 \\ {x}_2=1 \\ {y}_2=1 \\ {z}_2=1 \\ x={\displaystyle \frac{x_0+x_1+x_2}{3}}={\displaystyle \frac{3+1+1}{3}}={\displaystyle \frac{5}{3}}=1\frac{2}{3}=1.6667 \end{gathered}$$

$y={\displaystyle \frac{y_0+y_1+y_2}{3}}={\displaystyle \frac{2+(-2)+1}{3}}={\displaystyle \frac{1}{3}}=0.3333$

$z={\displaystyle \frac{z_0+z_1+z_2}{3}}={\displaystyle \frac{0+4+1}{3}}={\displaystyle \frac{5}{3}}=1\frac{2}{3}=1.6667$

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