# The slope of any line which is perpendicular to the x-axis is ____

A. 0

B. 1

C. -1

D. Not defined

Answer

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Hint: If we remember the plotting graph then we can remember that perpendicular to x-axis we have y-axis. Therefore, we need to find out the slope of the y-axis in order to solve this question. To calculate slope of a line we have the following formula- $m=\tan \theta $ where m=slope and $\theta $ is the smallest angle which the given line makes with the positive direction of x-axis.

“Complete step-by-step answer:”

The angle between the positive direction of x-axis and positive direction of y-axis is $\dfrac{\pi }{2}$ . Therefore, the slope of the positive y-axis is given by $m=\tan \dfrac{\pi }{2}$ which is not defined.

And the angle between the negative direction of y-axis and positive x-axis is $\dfrac{3\pi }{2}$ . Therefore, the slope of the negative y-axis is $m=\tan \dfrac{3\pi }{2}$ which is again undefined.

Hence, the correct option is option D.

Note: We also have the following result for perpendicular lines:

If ${{m}_{1}}$ is the slope of first line and ${{m}_{2}}$ is the slope of second line then if the lines are perpendicular ${{m}_{1}}\cdot {{m}_{2}}=-1$ .

But as we can see this result is not applicable to x-axis and y-axis because we have slope of x-axis=0 and y-axis=not defined. Therefore, we cannot multiply them and their multiplication is not equal to -1. But this is the only exception for this rule for lines in 2-D planes.

“Complete step-by-step answer:”

The angle between the positive direction of x-axis and positive direction of y-axis is $\dfrac{\pi }{2}$ . Therefore, the slope of the positive y-axis is given by $m=\tan \dfrac{\pi }{2}$ which is not defined.

And the angle between the negative direction of y-axis and positive x-axis is $\dfrac{3\pi }{2}$ . Therefore, the slope of the negative y-axis is $m=\tan \dfrac{3\pi }{2}$ which is again undefined.

Hence, the correct option is option D.

Note: We also have the following result for perpendicular lines:

If ${{m}_{1}}$ is the slope of first line and ${{m}_{2}}$ is the slope of second line then if the lines are perpendicular ${{m}_{1}}\cdot {{m}_{2}}=-1$ .

But as we can see this result is not applicable to x-axis and y-axis because we have slope of x-axis=0 and y-axis=not defined. Therefore, we cannot multiply them and their multiplication is not equal to -1. But this is the only exception for this rule for lines in 2-D planes.

Last updated date: 17th Sep 2023

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