Question

I : Length of the perpendicular from $(x_1,y_1)$ to the line $ax+by+c=0$ is $\left|\frac{a{x}_1+b{y}_1+c}{\sqrt{a^2+b^2}}\right|.$
II : The equation of the line passing through $(0,0)$ and perpendicular to $ax+by+c=0$ is $bx-ay=0.$ Then which of the following is true?

• A. only I
• B. only II
• C. both I & II
• D. neither I nor II

Answer 1

The correct option is C both I & II

$I.$ is true [formula of perpendicular distance]

$II.$ Equation of line pass through $(0,0)$ and perpendicular through $ax+by+c=0$ is $(y-0)=\frac{+b}{a}(x-0)$

(Using $m_1.m_2=-1$)

$ay=bx\Rightarrow bx-ay=0$

$II$ is true.