What is the orthocenter of a triangle with vertices A(−3,−2)A(−3,−2), B(−2,2)B(−2,2), and C(2,−2)C(2,−2)?
1 answer:
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 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):
For the y coordinate of the orthocenter we substitute in x=-2.
So the orthocenter is (x,y)=(-2,-1)
Answer: (-2,-1)
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