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# The slope of any line which is perpendicular to the x-axis is ____A. 0B. 1C. -1D. Not defined

Last updated date: 19th Sep 2024
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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.
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.
If ${{m}_{1}}$ is the slope of first line and ${{m}_{2}}$ is the slope of second line then if the lines are perpendicular ${{m}_{1}}\cdot {{m}_{2}}=-1$ .