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.

Answer 1

We have A(a, 1, 3), B(−2, b −5) and C (4, 7, c)
Now,
$$\begin{gathered} \frac{a-2+4}{3}=0,\frac{1+b+7}{3}=0\mathrm{and}\frac{3-5+c}{3}=0 \\ \Rightarrow a=-2,b=-8\mathrm{and}c=2 \end{gathered}$$