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Question
Find the slope of a line (i) which bisects the first quadrant angle (ii) which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.
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Solution
(i) We know that the angle between the coordinate axes is \[\frac{\pi}{2}\] .
The line bisects the first quadrant angle.
Inclination of the line with the positive x-axis = \[\frac{1}{2}\left( \frac{\pi}{2} \right) = \frac{\pi}{4}\]
\[\therefore \text { Slope of the line } = \tan\left( \frac{\pi}{4} \right) = 1\]
(ii) The line makes an angle of \[{30}^\circ\] with the positive direction of the y-axis measured anticlockwise
Since the line makes an angle of \[{30}^\circ\] with the positive direction of the y-axis measured anticlockwise, it makes an angle of \[{90}^\circ + {30}^\circ = {120}^\circ\] with the positive direction of the x-axis measured anticlockwise.
\[\therefore \text { Slope of the line } = \tan {120}^\circ = - \tan {60}^\circ = - \sqrt{3}\]
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