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Home » Find the slopes of a line (i) which bisects the first quadrant angle (ii) which makes an angle of 300 with the positive direction of y – axis measured anticlockwise.
Find the slopes of a line (i) which bisects the first quadrant angle (ii) which makes an angle of 300 with the positive direction of y – axis measured anticlockwise.
CBSE | Class 11 | Exercise 23.1 | Maths | RD Sharma | Straight Lines
Find the slopes of a line (i) which bisects the first quadrant angle (ii) which makes an angle of 300 with the positive direction of y – axis measured anticlockwise.

(i) Which bisects the first quadrant angle?

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

    \[x\text{ }\text{ }axis\]

Since, angle

    \[=\text{ }90/2\text{ }=\text{ }{{45}^{o}}~\]

By using the formula,

The slope of the line,

    \[m\text{ }=\text{ }tan~\theta \]

The slope of the line for a given angle is

    \[m\text{ }=\text{ }tan\text{ }{{45}^{o}}\]

So,

    \[m\text{ }=\text{ }1\]

∴ The slope of the line is

    \[1\]

(ii) Which makes an angle of

    \[{{30}^{0}}\]

 with the positive direction of

    \[y\text{ }\text{ }axis\]

measured anticlockwise?

Given: The line makes an angle of

    \[{{30}^{o}}\]

 with the positive direction of

    \[y\text{ }\text{ }axis\]

We know that, angle between line and positive side of axis

    \[=>\text{ }{{90}^{o}}~+\text{ }{{30}^{o}}~=\text{ }{{120}^{o}}\]

By using the formula,

The slope of the line,

    \[m\text{ }=\text{ }tan~\theta \]

The slope of the line for a given angle is

    \[m\text{ }=\text{ }tan\text{ }{{120}^{o}}\]

So,

    \[m\text{ }=\text{ }-\text{ }\surd 3\]

∴ The slope of the line is

    \[-\text{ }\surd 3\]

i

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