Euler's line

Here are three ways to associate a point to a triangle. The vertices are movable. The whole picture can be moved or zoomed. For each point, make three general observations about how it is related to the triangle. Without invoking the "Constructions," can you guess how they are constructed? (There may be several equivalent constructions, each deserving attention!) Once you see the constructions, can you verify your observations? Can you suggest a relationship between the three points? This worksheet is a small modification of a worksheet of the same name created by Judah Schwartz: https://tube.geogebra.org/user/profile/id/25758