Find the coordinate of foot of the perpendicular from the point $(2, 1)$ to the line $2 x + y + 1 = 0$

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Solution

Foot of perpendicular from (2,1) to the line $2 x + y + 1 = 0$
$\frac{x - 2}{2} = \frac{y - 1}{1} = \frac{- 6}{2^{2} + 1^{2}}$
$\frac{x - 2}{2} = \frac{y - 1}{1} = \frac{- 6}{5}$
$x = \frac{- 6 \times 2}{5} + 2 = \frac{- 2}{5}, y = \frac{- 6}{5} + 1 = \frac{- 1}{5}$
Foot of perpendicular is $(\frac{- 2}{5}, \frac{- 1}{5})$

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