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MHT CET202526 Apr 2025Morning ShiftMathematicsStraight LinesActual

The line MN whose equation is x-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^ in anticlockwise direction. The equation of the line MN in the new position is

Options

  1. Ay =- 2
  2. By =2
  3. Cx=-2
  4. Dx=2

Correct answer

D. x=2

Step-by-step solution

The line MN is given by the equation x - y - 2 = 0 , which may be expressed as y = x - 2 with slope m₁ = 1 . This line intersects the X-axis at the point where y = 0 , giving x = 2 , so the point of rotation is M = (2, 0) . The initial line has an inclination of ₁ = 45^ since ₁ = 1 . Rotating anticlockwise by 45^ produces a new line with inclination ₂ = 90^ , which corresponds to a vertical line with undefined slope. The vertical line through (2, 0) has the equation x = 2 . Final Answer: D

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