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  • If is the orthocenter of the triangle ABC with vertices A (3, –7), B(&ndash

If (\alpha ,\beta ) is the orthocenter of the triangle ABC with vertices A (3, –7), B(–1,2) and C (4, 5), then 9 – 6 + 60
is equal to

Option: 1

30


Option: 2

35


Option: 3

40


Option: 4

25


Answers (1)

best_answer

\begin{aligned} & \text{Altitude of }B C=y+7=\frac{-5}{3}(x-3)\\ & 3 y+21=-5 x+15 \\ & 5 x+3 y+6=0\\ & \text{Altitude of } \mathrm{AC}: y-2=\frac{-1}{12}(\mathrm{x}+1)\\ & 12 y-24=-x-1 \\ & x+12 y=23 \\ & \alpha=\frac{-47}{19}, \quad \beta=\frac{121}{57} \\ & 9 a-6 \beta+60=25 \end{aligned}

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Divya Prakash Singh

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