Question

If the line joining two points A (2, 0) and B (3, 1) is rotated about A in anticlockwise direction through an angle of 15°, then the equation of the line in new position is ______.

विकल्प

• y = `-sqrt(3)x + 2sqrt(3)`

• y = 3x – 6

• y = `1/sqrt(3)x - 2/sqrt(3)`

• y = `sqrt(3)x - 2sqrt(3)`

Answer 1

If the line joining two points A (2, 0) and B (3, 1) is rotated about A in anticlockwise direction through an angle of 15°, then the equation of the line in new position is `underlinebb(y = sqrt(3)x - 2sqrt(3))`.

Explanation:

The slope of the line is `(y_2 - y_1)/(x_2 - x_1) = (1 - 0)/(3 - 2)` = 1 or tan 45° rotated anti-clockwise directlon the line through 15° the slope of line AD in new position.

New position will be tan 60° = `sqrt(3)`.

Therefore, the equation of the new line AD is

y – 0 = `sqrt(3)(x - 2)`

y = `sqrt(3)x - 2sqrt(3)`