+355 A median of a triangle is a line segment joining a vertex of a triangle to the midpoint of the opposite side. Let's try this out with a particular triangle. Consider the triangle \(ABC \) with \(A = (5,4), B = (-9, 6), C = (1, -4)\).
(a) Let \(D, E, F\) be the midpoints of \(\overline{BC},\overline{AC},\overline{AB}\) respectively. Find the equations of medians and \(\overline{AD}, \overline{BE},\overline{CF}.\)
(b) Show that the three medians in part (a) all pass through the same point.
