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COMEDK20269 May 2026Morning ShiftMathematicsStraight LinesActual

Find the co-ordinates of the orthocentre of the triangle formed by the lines L₁: y - x = 2 L₂: y + 2x = 8 L₃: 3y - x = 18

Options

  1. A( 10 7 , 40 7 )
  2. B(2, 4)
  3. C(6, 8)
  4. D( 22 7 , 43 7 )

Correct answer

A. ( 10 7 , 40 7 )

Step-by-step solution

The vertices of the triangle are the points of intersection of the given lines. Solving L₁ and L₂ : y - x = 2 and y + 2x = 8 x = 2, y = 4 . Let A (2, 4) . Solving L₁ and L₃ : y - x = 2 and 3y - x = 18 x = 6, y = 8 . Let C (6, 8) . The slope of L₃ (line BC ) is 1 3 . The altitude from A to BC is perpendicular to L₃ , so its slope is -3 . Equation of the altitude from A(2, 4) is: y - 4 = -3(x - 2) 3x + y = 10 The slope of L₂ (line AB ) is -2 . The altitude from C to AB is perpendicular to L₂ , so its slope is 1 2 . E

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