A line passing through the point (3,0)makes an angle with 30degree with +ve direction of x-axis.

If this line is rotated through an angle of 15degree in clockwise direction , find its equation in new position.

Question

A line passing through the point (3,0)makes an angle with
30degree with +ve direction of x-axis
If this line is rotated through an angle of 15degree in
clockwise direction , find its equation in new position

Gursheen kaur. · Accepted Answer

First of all we have to find the slope of the line

slope(m) = tan of the angle

⇒ tan 30 = 1/√3

The point where the line passes through is( $x_{1}, y_{1}$ ).
In this case,

$x_{1} = 3, y_{1} = 0$

The equation for the equation of a line is:

$y - y_{1} = m (x - x_{1}) \Rightarrow y - 0 = \frac{1}{\sqrt{3}} (x - 3) \Rightarrow y = \frac{1}{\sqrt{3}} (x - 3) \Rightarrow \sqrt{3} y = x - 3 \Rightarrow \sqrt{3} y - x + 3 = 0$

Now,

When the line is rotated through an angle of 15degree in clockwise direction

The new angle = ${30^{0} + 15^{0} = 45}^{0}$

slope(m) = tan of the angle

$\Rightarrow m = {\tan 45}^{0} \Rightarrow m = 1$

The equation for the equation of a line is:

$y - y_{1} = m (x - x_{1}) \Rightarrow y - 0 = 1 (x - 3) \Rightarrow y = (x - 3) \Rightarrow y - x + 3 = 0$

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A line passing through the point (3,0)makes an angle with 30degree with +ve direction of x-axis. If this line is rotated through an angle of 15degree in clockwise direction , find its equation in new position.

A line passing through the point (3,0)makes an angle with 30degree with +ve direction of x-axis.

If this line is rotated through an angle of 15degree in clockwise direction , find its equation in new position.