Question

If the ratio in which the XY plane divides the line joining the points (2, 4, 5) and (–4, 3, –2) is k: 1, then find the value of 10k is

• A. 25
• B. 35
• C. 40
• D. 100

Answer 1

The correct option is A 25

Let xy plane divide the line joining the points in the ratio k : 1
If the point divides the join of the given points in the ratio k:1, then
Z-coordinate of the point is given by $\frac{k(-2)+1\left(5\right)}{k+1}$

For a point on XY plane, z-coordinate must be zero.
$\Rightarrow –2k+5=0$
$\Rightarrow 2k=5$
$\Rightarrow k=\frac{5}{2}=2.5$
$\Rightarrow 10k=25$