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

A. 0

B. 1

C. -1

D. Not defined

Last updated date: 24th Mar 2023

•

Total views: 306k

•

Views today: 3.82k

Answer

Verified

306k+ views

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.

Recently Updated Pages

If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

A rod AB of length 4 units moves horizontally when class 11 maths JEE_Main

Evaluate the value of intlimits0pi cos 3xdx A 0 B 1 class 12 maths JEE_Main

Which of the following is correct 1 nleft S cup T right class 10 maths JEE_Main

What is the area of the triangle with vertices Aleft class 11 maths JEE_Main

KCN reacts readily to give a cyanide with A Ethyl alcohol class 12 chemistry JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?