The following GoeGebra applets show the construction procedure for the Euler Line in the Euclidean and Minkowskian spaces.
You can compare both procedures step by step
The Euler Line joins the following three notable points of a triangle:
-Orthocenter (where the Altitudes meet): Green colour
-Centroid (where the medians meet): Yellow colour
-Circumcenter (where the mediatrices meet): Pink colour
Drag the vertexes to change the shape of the triangle and the position of all the points.
EUCLIDEAN PLANE
MINKOWSKIAN PLANE
Following the same procedure but using different tools (the "normal" Geogebra tools for the Euclidean case, and their corresponding "spacetime" tools for the Minkowskian case) renders completely equivalent geometric results.