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  • A point R with x-coordinate 4 lies on the line segment joining the points P(2, minus 3, 4) and Q (8, 0, 10). Find the coordinates of the point R.

5.   A point R with x-coordinate 4 lies on the line segment joining the points P(2, –3, 4) and Q (8, 0, 10). Find the coordinates of the point R.  [Hint Suppose R divides PQ in the ratio k : 1. The coordinates of the point R are givenby

\left ( \frac{8k + 2 }{k+1}, \frac{-3}{k+1}, \frac{10 k + 4 }{k+1} \right ) 

Answers (1)

best_answer

Let R divides PQ in the ratio k: 1.

The coordinates of the point R are given   by

\left ( \frac{8k + 2 }{k+1}, \frac{-3}{k+1}, \frac{10 k + 4 }{k+1} \right ) 

now, as given the x coordinate of the R is 4.

So,

\frac{8k+2}{k+1}=4

k=\frac{1}{2}

Hence the coordinates of R are:

\left ( \frac{8\times\frac{1}{2} + 2 }{\frac{1}{2}+1}, \frac{-3}{\frac{1}{2}+1}, \frac{10 \times \frac{1}{2}+ 4 }{\frac{1}{2}+1} \right )=(4,-2,6)

Posted by

Pankaj Sanodiya

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