Question

The line joining two points \( A(2,0) \), \( B(3,1) \) is rotated about \( A \) in anti-clockwise direction through an angle of \( 15^\circ \). The equation of the line in the new position is

• A. \( \sqrt{3}x - y - 2\sqrt{5} = 0 \)
• B. \( x - 3y - 2 = 0 \)
• C. \( \sqrt{3}x + y - 2\sqrt{5} = 0 \)
• D. \( x + y - 2 = 0 \)

Hint:

To rotate a line, use the rotation transformation for coordinates: \( x' = x \cos \theta - y \sin \theta \), \( y' = x \sin \theta + y \cos \theta \).

Answer 1

The Correct Option is A

Step 1: Rotating the line.
The new equation after rotating the line can be obtained using the rotation formula for coordinates. After applying the transformation, the equation becomes \( \sqrt{3}x - y - 2\sqrt{5} = 0 \).

Step 2: Conclusion.
The new equation of the line is \( \sqrt{3}x - y - 2\sqrt{5} = 0 \), corresponding to option (1).