Question

The perpendicular distance from the point $(1, -1)$ to the line $x + 5y - 9 = 0$ is equal to

• A. $\sqrt{\frac{2}{13}}$
• B. $\sqrt{\frac{13}{2}}$
• C. $\frac{13}{2}$
• D. $\frac{2}{13}$

Answer 1

Answer: (B)

$\sqrt{\frac{13}{2}}$

Answer 2

$\because$ Perpendicular distance from $\left(x_{1}, y_{1}\right)$ to the line $a x+b y+c=0$ is
$d=\frac{\left|a x_{1}+b y_{1}+c\right|}{\sqrt{a^{2}+b^{2}}}$
$\therefore$ Required distance,
$d =\frac{|1+5(-1)-9|}{\sqrt{1^{2}+5^{2}}}$
$=\frac{|1-14|}{\sqrt{1+25}}=\frac{13}{\sqrt{26}}$
$=\sqrt{\frac{13}{2}}$