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
$(\frac{k x_{2} + x_{1}}{k + 1}, \frac{k y_{2} + y_{1}}{k + 1}, \frac{k z_{2} + z_{1}}{k + 1})$

Open in App

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.

Suggest Corrections

Similar questions

A point P divides the line segment joining the points A (3, -5) and B (-4, 8) such that $\frac{A P}{P B} = \frac{k}{1} .$ If P lies on the line x + y = 0, then find the value of k.

Q. Find the ratio in which point P(k, 7) divides the segment joining A(8, 9) and B(1, 2). Also find k.

A point P divides the line segment joining the points $A (3, - 5)$ and $B (- 4, 8)$ such that $\frac{A P}{B P} = \frac{K}{1}$ . If P lies on the line $x + y = 0,$ then fine the value of K.

Q. A point P divides the line segment joining the points A(3, −5) and B(−4, 8) such that

\frac{AP}{PB} = \frac{k}{1} .

If P lies on the line x + y = 0, then find the value of k. [CBSE 2012]

Q. Point P divides the line segment joining the points A (-1,3) and B (9,8) such that

\frac{A P}{B P} = \frac{k}{1}

. If P lies on the line x - y + 2=0, find the value of k.

Join BYJU'S Learning Program

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.