Question

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

• A. 5x + y + 10 = 0
• B. 5x - y + 20 = 0
• C. 5x - y - 10 = 0
• D. 5x + y + 20 = 0
• E. 5y - x - 10 = 0

Answer 1

Answer: (B)

$E$ 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
$y-5=5(x-(-3))$
$\Rightarrow y-5=5(x+3)$
$\Rightarrow y-5=5x+15$
$\Rightarrow 5x-y+20=0$