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JEE Main201910 Jan 2019Evening ShiftMathematicsStraight LinesActual

Two vertices of a triangle are 0 , 2 and 4 , 3 . If its orthocenter is at the origin, then its third vertex lies in which quadrant?

Options

  1. AFourth
  2. BSecond
  3. CThird
  4. DFirst

Correct answer

B. Second

Step-by-step solution

Let the third vertex be h , k . Since H is orthocenter of Δ A B C Since the slope of B H is 3 4 hence the slope of A C will be - 4 3 ⇒ Equation of line A C is 4 x + 3 y = 6     . . . 1 Similarly, since A H is parallel to y - axis hence B C will be parallel to x - axis and Equation of line B C is y = 3     . . . 2 On solving 1 and 2 h = - 3 4 ,   k = 3 ∴   The point C h , k ≡ - 3 4 , 3 lies in the 2 nd quadrant.

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