Question

The coordinates of the foot of the perpendicular from the point $(2,3)$ on the line $-y+3x+4=0$ are given by

• A. $(\frac{37}{10},-\frac{1}{10})$
• B. $(-\frac{1}{10},\frac{37}{10})$
• C. $(\frac{10}{37},-10)$
• D. $(\frac{2}{3},-\frac{1}{3})$

Answer 1

The correct option is B $(-\frac{1}{10},\frac{37}{10})$

Formula for foot of perpendicular from point $(h,k)$ on line$ax+by+c=0$ is $:\frac{x-h}{a}=\frac{y-k}{b}=-\frac{ah+bk+c}{a^2+b^2}$
where $(x,y)$ are co-ordinates of foot of perpendicular
$\therefore D\equiv (h,k):\frac{x-2}{3}=\frac{y-3}{-1}=-\frac{6-3+4}{9+1}$
$⟹x=2-\frac{3\times 7}{10}=\frac{-1}{10},y=3+\frac{7}{10}=\frac{37}{10}$