QJEEM23Maeba1: JEE Main 2023 Mathematics - Class 11 JEEM23Maeba1 Solution: If is the orthocenter of the triangle with vertices and , then…

Question

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If

(\alpha, \beta)

is the orthocenter of the triangle

\mathrm{ABC}

with vertices

A(3,-7), B(-1,2)

and

C(4,5)

, then

9 \alpha-6 \beta+60

is equal to :

Accepted Answer

\begin{aligned} Altitude of BC: y + 7 = \frac{- 5}{3} (x - 3) \\ 3 y + 21 = - 5 x + 15 \\ 5 x + 3 y + 6 = 0 \\ Altitude of AC: y - 2 = \frac{- 1}{12} (x + 1) \\ 12 y - 24 = - x - 1 \\ x + 12 y = 23 \\ α = \frac{- 47}{19}, β = \frac{121}{57} \\ 9 α - 6 β + 60 = 25 \end{aligned}

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