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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).
Solution
Let the coordinates of third vertex be (x1, y1, z1)
Now,
\[\frac{x_1 + 3 + 3}{3} = 0, \frac{y_1 - 5 + 0}{3} = 0 \text{ and } \frac{z_1 + 7 + 1}{3} = 0\]
\[ \Rightarrow x_1 = - 6, y_1 = 5 \text{ and } z_1 = - 8\]
Hence, the coordinates of third vertex of a triangle is (−6, 5, −8).
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