Question

The image of the origin in the line joining the points $(-9,4,5)$ and $(11,0,-1)$ is

• A. $(2,4,4)$
• B. $(1,2,2)$
• C. $(1,2,3)$
• D. $(2,2,1)$

Answer 1

Answer: (A)

$(2,4,4)$

Let $BC$ be the given line
Let there be a point $D$ on $BC$ such that $OD$ is perpendicular to $BC$.
Any general point on $BC$ can be written as $(-9+20k,4-4k,5-6k)$
Now dr's of $BC=(20,-4,-6)$,
dr's of $OD=(-9+20k,4-4k,5-6k)$
Since $OD$ is perpendicular to $BC,OD.BC=0$
$-180+400k-16+16k-30+36k=0$ i.e $k=0.5$
Putting the value of $k$ back in $D$,
$D(1,2,2)$
Let the image of the origin in line $BC$ be $E$.
Since $E$ is the mid point of $OD$ we get $E$ to be $(2,4,4)$.