Question

7x+y-10=0.x-2y+5=0,x+y+2=0.Find orthocenter.
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Answer 1

Answer:

Given lines are $7x + y – 10 = 0 → (1), x – 2y + 5 = 0 → (2), x + y + 2 = 0 → (3)$

Point of intersection of (2) and (3) is B (–3, 1)

Equation of the altitude through B is (x + 3) – 7(y – 1) = 0  

$⇒ x – 7y + 10 = 0 → (4)$

Point of intersection of (3) and (1) is C(2, –4)

Equation of the altitude through C is 2(x – 2) + (y + 4) = 0

$⇒ 2x + y = 0 → (5)$

Solving (4) and (5), orthocenter is (- 2/3, 4/3).