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AP EAMCET2009MathematicsStraight Lines

The point on the line 3 x+4 y=5 which is equidistant from (1,2) and (3,4) is

Options

  1. A(7,-4)
  2. B(15,-10)
  3. C(1 / 7,8 / 7)
  4. D(0,5 / 4)

Correct answer

B. (15,-10)

Step-by-step solution

Let point (x₁, y₁ ) be on the line 3 x+4 y=5 . Also, (x₁-1 )^2+ (y₁-2 )^2= (x₁-3 )^2 aligned &+ (y₁-4 )^2 x₁^2+y₁^2-2 x₁-4 y₁+5=x₁^2+ & y₁^2-6 x₁ & -8 y₁+25 aligned On solving Eqs. (i) and (ii), we get x₁=15, y₁=-10

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