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JEE Main20248 Apr 2024Morning ShiftMathematicsStraight LinesActual

The equations of two sides AB and AC of a triangle ABC are 4 x+y=14 and 3 x-2 y=5 , respectively. The point (2,- 4 3 ) divides the third side BC internally in the ratio 2: 1 . the equation of the side BC is

Options

  1. Ax+3 y+2=0
  2. Bx-6 y-10=0
  3. Cx-3 y-6=0
  4. Dx+6 y+6=0

Correct answer

A. x+3 y+2=0

Step-by-step solution

aligned & 2 x ₂+ x ₁ 3 =2, 2 ( 3 x ₂-5 2 )+ (14-4 x ₁ ) 3 = -4 3 & 2 x ₂+ x ₁=6,3 x ₂-4 x ₁=-13 & x ₂=1, x ₁=4 aligned So, C (1,-1), B (4,-2) m = -1 3 Equation of BC : y +1= -1 3 ( x -1) aligned & 3 y+3=-x+1 & x+3 y+2=0 aligned

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