Find the slopes of a line(i) which bisects the first quadrant angle(ii

1.	Find the slopes 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» (i) Given: Line bisects the first quadrant We know that, if the line bisects in the first quadrant, then the angle must be between line and the positive direction of x – axis. Since, angle = 90/2 = 45° By using the formula, The slope of the line, m = tan θ The slope of the line for a given angle is m = tan 45° So, m = 1 ∴ The slope of the line is 1. (ii) Given: The line makes an angle of 30° with the positive direction of y – axis. We know that, angle between line and positive side of axis => 90° + 30° = 120° By using the formula, The slope of the line, m = tan θ The slope of the line for a given angle is m = tan 120° So, m = – √3 ∴ The slope of the line is – √3.

Find the slopes 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»

(i) Given: Line bisects the first quadrant

We know that, if the line bisects in the first quadrant, then the angle must be between line and the positive direction of x – axis.

Since, angle = 90/2 = 45°

By using the formula,
The slope of the line, m = tan θ

The slope of the line for a given angle is m = tan 45°

So, m = 1

∴ The slope of the line is 1.

(ii) Given: The line makes an angle of 30° with the positive direction of y – axis.

We know that, angle between line and positive side of axis => 90° + 30° = 120°

By using the formula,
The slope of the line, m = tan θ

The slope of the line for a given angle is m = tan 120°

So, m = – √3

∴ The slope of the line is – √3.