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Question
Write the coordinates of the point P which is five-sixth of the way from A(−2, 0, 6) to B(10, −6, −12).
Solution
Let the coordinates of the point be P(x, y, z).
Now \[PA = \frac{5}{6}PB\]
\[ \Rightarrow \frac{PA}{PB} = \frac{5}{6}\]
\[ \therefore x = \frac{5 \times 10 - 6 \times 2}{5 + 6}, y = \frac{5 \times \left( - 6 \right) + 6 \times 0}{5 + 6}, z = \frac{5 \times \left( - 12 \right) + 6 \times 6}{5 + 6}\]
\[ \therefore x = \frac{38}{11}, y = \frac{- 24}{11}, z = \frac{- 34}{11}\]
Hence, the coordinates of the point is\[\left( \frac{38}{11}, \frac{- 24}{11}, \frac{- 34}{11} \right)\]
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