Question

The x-coordinate of a point on the line joining the points P(2, 2, 1) and Q(5, 1, -2) is 4. Find its z-coordinate.

Answer 1

Given: $P(2,2,1)\equiv (x_1,y_1,z_1)$and $Q(5,1,-2)\equiv (x_2,y_2,z_2)$

Let the point on the line joining P and Q $(x,y,z)$ divides it the ration of $m:1$ then

$x=\frac{m{x}_2+x_1}{m+1}$

$\Rightarrow 4=\frac{m\times 5+2}{m+1}$

$\Rightarrow 4m+4=5m+2$

$\Rightarrow m=2$

z-coordinate is: $z=\frac{m{z}_2+z_1}{m+1}$

$\Rightarrow z=\frac{2\times (-2)+1}{2+1}=-1$

$z=-1$