Expert: Sherry Wallin - 2/5/2009

Question
what is the formula to find the orthocentre of a triangle when 3 of its vertices are given

Answer
Hi Kavitha!
    I'm not aware of any direct 'formula' for finding the orthocenter of a triangle given only the vertices. What you need to do is to place the triangle on say the x-axis and put one of the vertices at (0,0). Essentially you need to find the equation of two of the medians of the altitudes from the vertices and set them equal to each other and solve for one of the variables and then substitute this value back into one of the equations you used to find the other variable. Here is a link to a web page that tells you all about it:

http://math.coe.uga.edu/jwilson/EMAT6680Fa05/Brown/triangle%20centers/trianglece...

Best of Luck,
Math Prof