Q. 44.4( 18 Votes )

# Find the slopes of a line

(i) which bisects the first quadrant angle

(ii) which makes an angle of 30^{0} 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 =

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^{o} with the positive direction of y - axis (Given)

Since Angle between line and positive side of axis = 90^{o} + 30^{o} = 120^{o}

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^{o}

m = – √3

Hence, The slope of the line is – √3 .

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