equation of sides of triangle areX+2y=0-----(1)4x+3y=5-----(2)3x+y=0------(3)So for orthocentercoordinates of triangle by intersection of equation are (0,0) by 1 and 3 equation.(2,-1) by 1 and 2 and (-1,3) by 2 and 3 equations.Now orthocenter is intersection point of altitudes on sides ,so By (2,-1) altitude is (y+1)=1/3(x-2)1/3 is slope of 3 equation ,and by(0,0) point altitude is (y-0)=3/4(x-0)where 3/4 is slope of 2 equation .So by this we get equation of altitudes ----- x-3y-3=0 and 3x-4y=0 And intersection of these altitude is orthocenter i.e (-12/5 , -9/5) ans.
