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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 ______.
Options
y = `-sqrt(3)x + 2sqrt(3)`
y = 3x – 6
y = `1/sqrt(3)x - 2/sqrt(3)`
y = `sqrt(3)x - 2sqrt(3)`
Solution
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)`
