TRIANGLE HELP

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.