Question

The nearest point on the line $3x+4y=12$ from the origin is

• A. $\left(\frac{36}{25},\frac{48}{25}\right)$
• B. $\left(3,\frac{3}{4}\right)$
• C. $\left(2,\frac{3}{2}\right)$
• D. None of these

Answer 1

Answer: (A)

If ‘$D$’ be the foot of altitude, drawn from origin to the given line, then ‘$D$’ is the required point.
Let $\angle OBA=\theta$
$\Rightarrow \tan \theta =4/3$
$\Rightarrow \angle DOA=\theta$
we have $OD=12/5$
If $D$ is $(h,k)$ then $h=OD\cos \theta ,k=OD\sin \theta$
$\Rightarrow h=36/25,k=48/25$.