How can do you find the orthocenter of a triangle...?

Question

when it has the points S (0,1), T (4,7) and U (8,-3). What formula would you use to first find the altitudes and then the coordinates of the orthocenter?

Answer 1

The formulas are rather complicated, surely not easy to remember.

You may find them in the paragraph
11. Plain Analytic Geometry
in this web-page:

http://www.cut-the-knot.org/triangle/altitudes.shtml

The orthocenter of our triangle is [1.25, 1.5].

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