Question

A point C with z-coordinate 8 lies on the line segment joining the points A(2, -3, 4) and B(8, 0, 10). Find its coordinates.

Answer 1

Suppose C divides AB in the ratio k : 1 The z coordinates of C is 8

$\therefore \frac{10k+4}{k+1}=8\Rightarrow 10k+4=8k+8$

$\Rightarrow 2k=4\Rightarrow k=2$

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

$\Rightarrow (\frac{8\times 2+2}{2+1},\frac{-3}{2+1},\frac{10\times 2+4}{2+1})$

$\Rightarrow (\frac{18}{3},\frac{-3}{3},\frac{24}{3})\therefore$

(6, -1, 8)

Hence, the coordinates of C are (6, -1, 8)