If the point P divides the line segment joining points A and B nternally in the ratio k : 1, then the coordinates of point P will be
$(\frac{k x_{2} + x_{1}}{k + 1}, \frac{k y_{2} + y_{1}}{k + 1}, \frac{k z_{2} + z_{1}}{k + 1})$

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Solution

Let Co-ordinate of P be (x , y, z) then
$x = \frac{k \times 3 + 1 \times - 2}{k + 1} = \frac{3 k - 2}{k + 1}$
$y = \frac{k \times - 5 + 1 \times 4}{k + 1} = \frac{- 5 k + 4}{k + 1}$
$z = \frac{k \times 8 + 7 \times 1}{k + 1} = \frac{8 k + 7}{k + 1}$
Use section formula.

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If the point P divides the line segment joining points A and B nternally in the ratio k : 1, then the coordinates of point P will be (kx2+x1k+1,ky2+y1k+1,kz2+z1k+1)

Let Co-ordinate of P be (x , y, z) then x=k×3+1×−2k+1=3k−2k+1 y=k×−5+1×4k+1=−5k+4k+1 z=k×8+7×1k+1=8k+7k+1 Use section formula.

If the point P divides the line segment joining points A and B nternally in the ratio k : 1, then the coordinates of point P will be
$(\frac{k x_{2} + x_{1}}{k + 1}, \frac{k y_{2} + y_{1}}{k + 1}, \frac{k z_{2} + z_{1}}{k + 1})$

Let Co-ordinate of P be (x , y, z) then
$x = \frac{k \times 3 + 1 \times - 2}{k + 1} = \frac{3 k - 2}{k + 1}$
$y = \frac{k \times - 5 + 1 \times 4}{k + 1} = \frac{- 5 k + 4}{k + 1}$
$z = \frac{k \times 8 + 7 \times 1}{k + 1} = \frac{8 k + 7}{k + 1}$
Use section formula.