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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 find the equation of the line in new position
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Solution
Slope of the line AB
m = tan θ = `(1 - 0)/(3 - 2)`
tan θ = 1
θ = 45°
∴ The line AB makes an angle 45° with x-axis.
Given that the line AB is rotated through an angle of 15° about the point A in the anticlockwise direction.
∴ The angle made by the new line AB’ is 45° + 15° = 60°
Slope of the new line AB’ is m1 = tan 60° = `sqrt(3)`
∴ The equation of the new line AB’ is the equation of the straight line passing through the point A(2, 0) and having slope m1 = `sqrt(3)`
y – 0 = `sqrt(3) (x - 2)`
y = `sqrt(3)x - 2sqrt(3)`
`sqrt(3)x - y - 2sqrt(3)` = 0
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