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JEE Main202528 Jan 2025Evening ShiftMathematicsStraight LinesActual

Two equal sides of an isosceles triangle are along -x+2 y=4 and x+y=4 . If m is the slope of its third side, then the sum, of all possible distinct values of m , is :

Options

  1. A-2 10
  2. B12
  3. C6
  4. D-6

Correct answer

C. 6

Step-by-step solution

Slope of the third side = slope of the perpendicular bisector of given lines h: -x+2 y-4 5 = x+y-4 2 aligned & h₁: 2 (-x+2 y-4)= 5 (x+y-4) & h₂: 2 (-x+2 y-4)=- 5 (x+y-4) & M_ L₁ :- [ 5 + 2 5 -2 2 ] & M_ L₂ :- [ 5 - 2 5 +2 2 ] & M_ L₁ +M_ L₂ =- [ 5 + 2 5 -2 2 + 5 - 2 5 +2 2 ] aligned aligned & =- [ ( 5 + 2 )( 5 +2 2 )+( 5 - 2 )( 5 -2 2 ) -3 ] & =6 aligned

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