Question

Find the coordinates of the point which divides the line segment joining the points (1,-2,3) and (3,4,-5) in the ratio 2:3 (i) internally, and (ii) externally.

Answer 1

(i) Internally: $h=\frac{m{x}_2+n{x}_1}{m+n}$, $k=\frac{m{y}_2+n{y}_1}{m+n}$, $l=\frac{m{x}_2+n{x}_1}{m+n}$

$h=\frac{2\left(3\right)+3\left(1\right)}{2+3},k=\frac{2\left(4\right)+3(-2)}{2+3},l=\frac{2(-5)+3\left(3\right)}{2+3}$

$h=\frac{9}{5},k=\frac{2}{5},l=\frac{-1}{5}$

$c(\frac{9}{5},\frac{2}{5},\frac{-1}{5})$.

(ii) Externally:

$h=\frac{m{x}_2-n{x}_1}{m-n},k=\frac{m{y}_2-n{y}_1}{m-n},l=\frac{m{x}_2-n{x}_1}{m-n}$

$h=\frac{2\left(3\right)-3\left(1\right)}{2-3},k=\frac{2\left(4\right)-3(-2)}{2-3},l=\frac{2(-5)-3\left(3\right)}{2-3}$

$h=\frac{3}{-1},k=\frac{14}{-1},l=\frac{-19}{-1}$

$c(-3,-14,19)$.