A median is the segment joining a vertex of a triangle to the midpoint of the opposite side. Remarkably, the three medians always meet at a single point (the centroid), and that point always divides each median in a 2:1 ratio measured from the vertex. Reshape the triangle and check whether this ratio really holds every time.
Why is it always 2:1? Physically, the centroid is the balance point of the triangle treated as a plate of evenly spread mass. A median is a line that cuts the triangle into exactly half the area (half the mass), and to balance at the point where the three medians meet, you have to support it where the weight on the vertex side is twice the weight on the midpoint side — which is why the ratio always comes out 2:1.
The coordinates of the centroid are just the average of the three vertex coordinates: G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3).