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Equation of a line after rotating it about a point on it

This type of question, asked 2 times: May 2021 S1, 26 Apr 2025 S1. All 3 questions below, oldest first.

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  1. Question 1

    May 2021 S1

    135
    If the line joining two points A(2,0)A(2,0) and B(3,1)B(3,1) is rotated about AA in anticlockwise direction through an angle of 15∘15^\circ, then the equation of the line in the new position is

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  2. Question 2

    May 2021 S1

    106
    A line through the point A(2,0)A(2,0) which makes an angle of 30∘30^\circ with the positive direction of X-axis is rotated about AA in clockwise direction through an angle of 15∘15^\circ. Then, the equation of the straight line in the new position is

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  3. Question 3

    26 Apr 2025 S1

    104
    The line MN whose equation is x−y−2=0x-y- 2 = 0 cuts the X -axis at M and co-ordinates of N are (4, 2). The line MN is rotated about M through 45∘45^{\circ} in anticlockwise direction. The equation of the line MN in the new position is

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