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-

(i) Line bisects first quadrant. ⇒ Angle between line and positive direction of x axis=90^∘/2=45^∘ Slope of line (m)=tanθ m=tan 45^∘ m=1 (ii) Line makes angle ...

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Standard XII

Mathematics

Slope of a Line

Find the slop...

Question

Find the slope of a line (i) which bisects the first quadrant angle (ii) which makes an angle of $30^{\circ}$ with the positive direction of y-axis measured anticlockwise.

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Solution

$(i) Line bisects first quadrant. \Rightarrow Angle between line and positive direction of x-axis = \frac{90^{\circ}}{2} = 45^{\circ} Slope of line (m) = t a n θ m = t a n 45^{\circ} m = 1 (ii) Line makes angle of 30^{\circ} with the positive direction of y-axis, = Angle between line and positive side of axis = 90^{\circ} + 30^{\circ} θ^{\circ} = 120^{\circ} m = t a n 120^{\circ} m = - \sqrt{3}$

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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.

(i) Line bisects first quadrant.⇒ Angle between line and positive direction of x-axis=90∘2=45∘Slope of line (m)=tanθm=tan 45∘m=1(ii) Line makes angle of 30∘ with the positive direction of y-axis,= Angle between line and positive side of axis=90∘+30∘θ∘=120∘m=tan120∘m=−√3

Find the slope of a line (i) which bisects the first quadrant angle (ii) which makes an angle of $30^{\circ}$ with the positive direction of y-axis measured anticlockwise.