Euler line of a triangle is the straight line that contains the circumcenter, the centroid, and the orthocenter of the triangle.
Recall... circumcenter is the point of concurrency of the perpendicular bisectors of a triangle;
centroid is the point of concurrency of the medians of a triangle;
orthocenter is the point of concurrency of the altitudes in a triangle.
The applet below shows the Euler line of triangle ABC that contains its centroid, G, circumcenter, J, and orthocenter, I.
Drag any of the vertices of triangle ABC and observe the movement of these points, G, J, and I, in relation to the corresponding change in the triangle.
In addition, compare the distances from the centroid to the orthocenter and from the centroid to the circumcenter.