how to find the othrocenter of a trianle whoose vertices are A(0,0) b(-1,3) c (2,-1)

Dear gaurav

Orthocenter is the point of intersection of altitude

so find the equation of line which is perpendicular to the line joing point (-1,3) and (2,-1) and passes through (0,0)

slope of the line BC  = -1/2

slope of the line perpendicular to it =2

so equation of line :   y-3 =2 (x+1)

                          or  2x-y +5=0

now find another line which is perpendicular to the line joing point (0,0) and (2,-1) and passes through (-1,-3)

slope of the line AC  = -4/3

slope of the line perpendicular to it =3/4

so equation of line :   y =3/4 x

                          or  3x-4y =0

solve these two equation

x=-4  , y =-3

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