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

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 To Find: Find the slope of the line. Here, If the line bisects in the first quadrant, then the angle must be between line and the positive direction of x - axis . Since, Angle = \(\frac{90}{2}\) = 45° The formula used: The slope of the line, m = tan θ Similarly, The slope of the line for a given angle is m = tan 45° m = 1 Hence, The slope of the line is 1. (ii) To Find: Find the slope of the line. Here, The line makes an angle of 30° with the positive direction of y - axis (Given) Since Angle between line and positive side of axis = 90° + 30°= 120° The formula used: The slope of the line, m = tan θ Similarly, The slope of the line for a given angle is m = tan 120° m = – √3 Hence, 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

To Find: Find the slope of the line.

Here, If the line bisects in the first quadrant, then the angle must be between line and the positive direction of x - axis .

Since, Angle = \(\frac{90}{2}\) = 45°

The formula used: The slope of the line, m = tan θ

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

m = 1

Hence, The slope of the line is 1.

(ii) To Find: Find the slope of the line.

Here, The line makes an angle of 30° with the positive direction of y - axis (Given)

Since Angle between line and positive side of axis = 90° + 30°= 120°

The formula used: The slope of the line, m = tan θ

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

m = – √3

Hence, The slope of the line is – √3