A median of a triangle is a line segment from a vertex of a triangle to the midpoint of the opposite side of the triangle. Below, the three medians of the black triangle are shown in red.

[asy]
pair A, B,C, X,Y, Z;
A = (0,0);
B = (1,0);
C = (0.3,0.8);
draw(A--B--C--A);
X = (B+C)/2;
Y = (A+C)/2;
Z = (A+B)/2;
draw(A--X, red);
draw(B--Y, red);
draw(C--Z, red);
dot(A^^B^^C^^X^^Y^^Z);
[/asy]

Notice that the three medians appear to pass through the same point! Let's test this out with a specific triangle. Consider one specific triangle $ABC$ with $A = (4,8)$, $B = (2,-6)$, and $C = (-4,4)$.

The three medians of this triangle meet at a point. What is that point?