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JEE Main202315 Apr 2023Morning ShiftMathematicsStraight LinesActual

If α , β is the orthocenter of the triangle A B C with vertices A 3 , – 7 , B – 1 , 2 and C 4 , 5 , then 9 α - 6 β + 60 is equal to

Options

  1. A25
  2. B35
  3. C30
  4. D40

Correct answer

A. 25

Step-by-step solution

The required diagram will be: Equation of A D : y + 7 = - 5 3 x - 3 ⇒ 3 y + 21 = - 5 x + 15 ⇒ 5 x + 3 y + 6 = 0   . . . . . . i Equation of B E : y - 2 = - 1 12 x + 1 ⇒ 12 y - 24 = – x - 1 ⇒ x = 23 - 12 y . . . . ( i i ) by ii 115 - 60 y + 3 y + 6 = 0 ⇒ 57 y = 121 y = 121 57 ,   x = 23 - 12 × 121 57 ∴   9 α - 6 β + 60 = 9 × 23 - 108 × 121 57 - 6 × 121 57 + 60 = 207 - 242 + 60 = 25 Hence this is the required option.

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