Repled at http://www.goiit.com/posts/list/0/geometry-how-we-find-the-orthocenter-if-three-vertex-are-given-73792.htm#363828

i can tell u a short cut for this."Elessar sir plz tell ur opinions on this.

i will try to xplain the procedure wid an example

Given the vertices are(1,-3),(6,1), and (4,-1)) shift the origin to (1,-3) by transformation of axes then the vertices are (0,0) (5,4) (3,2). First we hav to find Q

Q = x₁x₂+y₁y₂/x₁y₂-x₂y_{1 =} 15+8/10-12 = -23/2.

 Now before calculating ortho do this  [Q(y_2-y₁), -Q(x₂-x₁)] = [-23/2(-2), 23/2(-2)] = (23, -23)

therefore Ortho centre = [23+1, 23+(-3)] = (24, -26)........the last step is becoz we had transformed the origin if the vertices are lik (0,0) (x₁,y₁) (x₂,y₂) the last step can be omitted.