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Center of an n-gon?

  1. Jan 31, 2012 #1
    Let's say a city planner plans to place a fountain that is equidistant from where people will want to walk toward a water fountain (e.g, where a runner will likely stop along a trail and turn towards a water fountain). He identifies 7 such spots.

    How would the builder go about finding the spot for a water fountain?
     
  2. jcsd
  3. Jan 31, 2012 #2

    HallsofIvy

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    Set up a coordinate system giving (x,y) values to each of the points. The "centroid" will be the point whose x coordinate is the average of the 7 x values of the points and y coordinate will be the average of the 7 y values of the points.
     
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