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JEE Main20203 Sep 2020Evening ShiftMathematicsStraight LinesActual

If a ∆ A B C has vertices A – 1 , 7 , B – 7 , 1 and C 5 , – 5 , then its orthocentre has coordinates:

Options

  1. A–   3 , 3
  2. B3 , - 3
  3. C- 3 5 , 3 5
  4. D3 5 , - 3 5

Correct answer

A. –   3 , 3

Step-by-step solution

Slope of line B C is m B C = 6 - 12 = - 1 2 Slope of line A D = 1 m B C = 2 ∴ Equation of line A D is y - 7 = 2 x + 1 ⇒ y = 2 x + 9   . . . 1 Slope of line A C is m A C = 12 - 6 = - 2 Slope of line B E = 1 m A C = 1 2 ∴ Equation of B E is y - 1 = 1 2 x + 7 ⇒ y = x 2 + 9 2   . . . 2 Comparing equations 1   &   2 , we get 2 x + 9 = x + 9 2 ⇒ 4 x + 18 = x + 9 ⇒ 3 x = - 9 ⇒ x = - 3 ∴     y = 2 x + 9 = 3 Therefore, orthocentre has co-ordin

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