Question

The point of intersection of the line joining the points $(2,4,5)$ and $(-4,3,-2)$ and the xy plane is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Given points are $A(2,4,5)$ and $B(-4,3,-2)$. Let xy plane divide the

line joining the points in the ratio of k:1

For x-y plane, z-coordinate must be zero

$\frac{k(-2)+1\left(5\right)}{k+1}=0$

$-2k+5=0$

$2k=5$

$k=\frac{5}{2}$

So,xy plane divides the joining the points (2,4,5) and (-4,3,-2) in the ratio of 5:2

X-coordinate =$\frac{5(-4)+2\left(2\right)}{5+2}$

$\Rightarrow \frac{-20+4}{7}=\frac{-16}{7}$

Y-coordinate $y=\frac{5\left(3\right)+2\left(4\right)}{5+2}$

=$\frac{15+8}{7}=\frac{23}{7}$

Intersection of the line joining the points (2,4,5) and (-4,3,-2) and the xy plane is

$(\frac{-16}{7},\frac{23}{7},0)$