Question

Write the coordinates of third vertex of a triangle having centroid at the origin and two vertices at (3, −5, 7) and (3, 0, 1).

Answer 1

Let the coordinates of third vertex be (x₁, y₁, z₁)
Now,
$$\begin{gathered} \frac{x_1+3+3}{3}=0,\frac{y_1-5+0}{3}=0\mathrm{and}\frac{z_1+7+1}{3}=0 \\ \Rightarrow x_1=-6,y_1=5\mathrm{and}{z}_1=-8 \end{gathered}$$
Hence, the coordinates of third vertex of a triangle is (−6, 5, −8).