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.

Answer 1

(i) We know that the angle between the coordinate axes is $\frac{\mathrm{\pi }}{2}$.

The line bisects the first quadrant angle.

Inclination of the line with the positive x-axis = $\frac{1}{2}\left(\frac{\mathrm{\pi }}{2}\right)=\frac{\mathrm{\pi }}{4}$

$\therefore \mathrm{Slope}\mathrm{of}\mathrm{the}\mathrm{line}=\tan \left(\frac{\mathrm{\pi }}{4}\right)=1$

(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.

$\therefore \mathrm{Slope}\mathrm{of}\mathrm{the}\mathrm{line}=\tan {120}^{\circ }=-\tan {60}^{\circ }=-\sqrt{3}$