Question

The nearest point on the line $3x-4y=25$ from the origin is

• A. $(\frac{17}{3},-2)$
• B. $(\frac{25}{3},0)$
• C. $(11,2)$
• D. $(3,-4)$

Answer 1

The correct option is D $(3,-4)$

Nearest point from origin on a given line is its foot of perpendicular.
Let $P\equiv (\alpha ,\beta )$ be the nearest point on $3x-4y-25=0$ from $O\equiv (0,0)$
$\Rightarrow \frac{\alpha -0}{3}=\frac{\beta -0}{4}=-\frac{-\left(25\right)}{3^2+(-4{)}^2}=1$
$\Rightarrow \alpha =3,\beta =-4$
So, $P\equiv (3,-4$)