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JEE MainMathematicsStraight Lines

In a triangle ABC , the coordinates of the vertex A are (1, 2) . The equations of the perpendicular bisectors of the sides AB and AC are x - y + 3 = 0 and x + 2y - 10 = 0 , respectively. If the equation of the line BC is x - 2y + c = 0 , then the value of c is equal to:

Options

  1. A6
  2. B-3
  3. C9
  4. D12

Correct answer

C. 9

Step-by-step solution

The image of a vertex in the perpendicular bisector of an adjacent side gives the coordinates of the other vertex on that side. Let the coordinates of B be (x₁, y₁) . B is the image of A(1, 2) in the line x - y + 3 = 0 . x₁ - 1 1 = y₁ - 2 -1 = -2(1 - 2 + 3) 1^2 + (-1)^2 x₁ - 1 1 = y₁ - 2 -1 = -2(2) 2 = -2 x₁ - 1 = -2 x₁ = -1 y₁ - 2 = 2 y₁ = 4 So, B is (-1, 4) . Let the coordinates of C be (x₂, y₂) . C is the image of A(1, 2) in the line x + 2y - 10 = 0 . x₂ - 1 1 = y₂ - 2 2 = -2(1 + 4 - 10) 1^2 + 2^2 x₂ - 1 1 = y₂

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