Question

Equation of a line through the origin and perpendicular to the line joining $\left(a,0\right)$ and $\left(-a,0\right)$ is

• A. $y=0$
• B. $x=0$
• C. $a=–a$
• D. $y=–a$

Answer 1

The correct option is B

$x=0$

Evaluate the slope of the line:

The slope of the line passing through $(a,0)$ and $(-a,0)$ is $m=\frac{(y_2–y_1)}{(x_2–x_1)}$

$=\frac{0}{(-a–a)}$

$=0$

$\Rightarrow$It is the x-axis.

So, the required line passing through the origin and perpendicular to the x-axis is the y-axis.

$\therefore$As we know, the Equation of the y-axis is $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}$

Hence, Option ‘B’ is Correct.