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JEE Main20199 Jan 2019Evening ShiftMathematicsStraight LinesActual

Let the equations of two sides of a triangle be 3 x - 2 y + 6 = 0 and 4 x + 5 y - 20 = 0 . If the orthocenter of this triangle is at 1 , 1 then the equation of it's third side is:

Options

  1. A122 y + 26 x + 1675 = 0
  2. B26 x - 122 y - 1675 = 0
  3. C26 x + 61 y + 1675 = 0
  4. D122 y - 26 x - 1675 = 0

Correct answer

B. 26 x - 122 y - 1675 = 0

Step-by-step solution

To find equation of B C , first we will find coordinates of B and C . m A C = 3 2 A C and B B ' are perpendicular to each other hence m B B ' = - 2 3 Equation of line passing through x 1 , y 1 and having slope m is y - y 1 = m x - x 1 For equation of B B ' y - 1 = - 2 3 x - 1 ⇒ 2 x + 3 y = 5       . . . . . . . . 1 Point of intersection of A B and B B ' ⇒ B   35 2 ,   - 10 Similarly point C - 13 ,   - 33 2 Equation of B C is, y - y 1 = y 2 - y 1 x 2 - x 1 x

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