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AP EAMCET2005MathematicsStraight Lines

If P M is the perpendicular from P(2,3) onto the line x+y=3 , then the coordinates of M are

Options

  1. A(2, 1)
  2. B(−1,4)
  3. C(1, 2)
  4. D(4, −1)

Correct answer

C. (1, 2)

Step-by-step solution

Let the co-ordinates of M are (x₁, y₁ ) . Since the line P M is to the given line x+y=3 aligned & y₁-3 x₁-2 (-1)=1 & y₁-3=x₁-2 & aligned and also the points lies on the given line On solving Eqs. (i) and (ii), we get x₁=1, y₁=2 The co-ordinates of M are (1,2) .

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