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Mathematics
Problem
Show that the centroid of the triangle with vertices
A
(
x
1
,
y
1
,
z
1
)
A(x_1, y_1, z_1)
A
(
x
1
,
y
1
,
z
1
)
,
B
(
x
2
,
y
2
,
z
2
)
B(x_2, y_2, z_2)
B
(
x
2
,
y
2
,
z
2
)
and
C
(
x
3
,
y
3
,
z
3
)
C(x_3, y_3, z_3)
C
(
x
3
,
y
3
,
z
3
)
has the coordinates
(
x
1
+
x
2
+
x
3
3
,
y
1
+
y
2
+
y
3
3
,
z
1
+
z
2
+
z
3
3
)
\left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}, \frac{z_1 + z_2 + z_3}{3} \right)
(
3
x
1
+
x
2
+
x
3
,
3
y
1
+
y
2
+
y
3
,
3
z
1
+
z
2
+
z
3
)
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