Question

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

Answer 1

Answer:

Please refer to the above pic attached.

Hope it helps you.

Mark it as a Brainliest Answers !

Answer 2

Given:

• A line passes through points (3,0)
• Angle formed = 30°
• The angle of rotation of the line = 15°

To Find:

• Equation of a line in its new position.

Solution:

First, let us draw a diagram using the given information.

In the diagram, the line passes through A(3,0) in a positive direction of the x-axis forming an angle of 30°. After rotating the line 15 ° clockwise we get a new angle.

Let us consider the new angle as our slope "m",

∴ Slope, m =  (√3 - 1)/(√3 + 1) = tan 15° = 2 - √3

The general form of the equation of a line passing through points (x,y) is given by,

⇒ y-$y_1$ = m(x-$x_1$)

Now the equation of the line passing through (3,0) is given by,

⇒ y - 0 = 2 - √3(x - 3)

⇒ y = (2-√3)x - 6 + 2√3

∴ The equation of the line passing through the points (3,0) is, y = (2-√3)x - 6 + 2√3.