Question

Find the ratio in which the YZ-plane divides the line segment formed by joining the points $(-2,4,7)$ and $(3,-5,8).$

Answer 1

Let the line joining the points $A(-2,4,7)$ and $B(3,-5,8)$ be divided by the yz plane at a point C in the ratio k : 1.

Then coordinates of C are

$(\frac{3k-2}{k+1},\frac{-5k+4}{k+1},\frac{8k+7}{k+1})$

Since the point C lies on yz-plane. So $x=0$

$\therefore \frac{3k-2}{k+1}=0\Rightarrow 3k-2=0\Rightarrow k=\frac{2}{3}$

Thus the required ratio is $\frac{2}{3}i.e.2:3.$