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Let the vertex A of a triangle ABC be (3, 4) . If the equations of the perpendicular bisectors of the sides AB and AC are x - y + 2 = 0 and 2x + y - 5 = 0 respectively, then the equation of the side BC is:

Options

  1. Ax - y + 2 = 0
  2. Bx - y + 3 = 0
  3. Cx - y - 1 = 0
  4. Dx - 2y + 5 = 0

Correct answer

B. x - y + 3 = 0

Step-by-step solution

The perpendicular bisector of a side of a triangle acts as a line of symmetry for the two vertices on that side. Thus, vertex B is the image of vertex A with respect to the perpendicular bisector of AB , and vertex C is the image of A with respect to the perpendicular bisector of AC . Let B (x₁, y₁) . Using the image formula for A(3, 4) in the line x - y + 2 = 0 : x₁ - 3 1 = y₁ - 4 -1 = -2 ( 3 - 4 + 2 1^2 + (-1)^2 ) x₁ - 3 1 = y₁ - 4 -1 = -2 ( 1 2 ) = -1 x₁ - 3 = -1 x₁ = 2 y₁ - 4 = 1 y₁ = 5 Thus, B (2, 5) . Let C (

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