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Q. The equation of the line passing through $(- 3, 5)$ and perpendicular to the line through the points $(1, 0)$ and $(- 4, 1)$ is

KEAMKEAM 2017Straight Lines

Solution:

$E$ slope of the line passing through $(1,0)$ and
$(-4,1)=\frac{1-0}{-4-1}=\frac{-1}{5}$
$\therefore $ Slope of line perpendicular to the above line
$=\frac{-1}{\left(-\frac{1}{5}\right)}=5$
$\therefore $ Equation of required line is given by
$ y-5=5(x-(-3)) $
$\Rightarrow y-5=5(x+3)$
$\Rightarrow y-5=5 x+15$
$\Rightarrow 5 x-y+20=0$