A(−3,−2), B(−2,2), C(2,−2)
The orthocenter is the meet of the altitudes. We see AC is parallel to the x axis so the perpendicular [tex]x=-2[/tex] is the altitude through B.
Between A and B we have slope (2 - -2)/(-2 - -3) = 4 so perpendicular slope -1/4 through C(2,-2):
[tex]y+2 = -\frac 1 4 (x - 2)[/tex]
For the y coordinate of the orthocenter we substitute in x=-2.
[tex]y+2 = -\frac 1 4(-2 - 2) = 1[/tex]
[tex]y = -1[/tex]
So the orthocenter is (x,y)=(-2,-1)
Answer: (-2,-1)
