The equation of a line passing through the point $(7,-4)$ and perpendicular to the line passing through the…
The equation of a line passing through the point $(7,-4)$ and perpendicular to the
line passing through the points $(2,3)$ and $(1,-2)$ is
$x+5 y+13=0$
$x-5 y-13=0$
$x-2 y-15=0$
$x+2 y+1=0$
Solution
Slope of line through $(2,3)$ and $(1,-2)$ is $\frac{-2-3}{1-2}=5$
Hence slope of required line is $-\frac{1}{5}$
Equation of required line is
$(y+4)=-\frac{1}{5}(x-7) \Rightarrow 5 y+20=-x+7 \text { i.e. } x+5 y+13=0$