If (a,b) be the orthocentre of the triangle whose vertices are (1,2) , (2,3) and (3,1) and ...

Question

If (a,b) be the orthocentre of the triangle whose vertices are (1,2) , (2,3) and (3,1)

Answer 1

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Let H (a,b) is orthocenter of the triangle who vertices are A(1,2) B(2,3) and C(3,1) 

Slope of AH * Slope of BC = -1 

(b-2)/(a-1) * 2/(-1) = -1 

2b-4 = a -1 

a – 2b + 3 = 0 …. Eqn 1 

Slope of BH * Slope of AC = -1 

(b-3)/(a-2) * 1/(-2) = -1 

b-3 = 2a – 4 

2a - b -1 = 0 …. Eqn 2 

Solving Eqn 1 and Eqn 2 

a = 5/3 and b = 7/3 then a + b = 4 

Now