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Question
If the origin is the centroid of a triangle ABC having vertices A(a, 1, 3), B(−2, b −5) and C (4, 7, c), find the values of a, b, c.
Solution
We have A(a, 1, 3), B(−2, b −5) and C (4, 7, c)
Now,
\[\frac{a - 2 + 4}{3} = 0, \frac{1 + b + 7}{3} = 0 \text{ and } \frac{3 - 5 + c}{3} = 0\]
\[ \Rightarrow a = - 2, b = - 8 \text{ and } c = 2\]
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