(I WILL GIVE BRAINLIEST AND 50 POINTS) A median of a triangle is a line segment joining a vertex of a triangle to the midpoint of the opposite side. The three medians of a triangle are drawn below.
Note that the three medians appear to intersect at the same point! Let's try this out with a particular triangle. Consider the triangle ABC with A = (3,6), B = (-5,2), and C = (7,-8).

(a) Let D, E, F be the midpoints of \overline{BC}, \overline{AC}, \overline{AB}, respectively. Find the equations of medians \overline{AD}, \overline{BE}, and \overline{CF}

(b) Show that the three medians in part (a) all pass through the same point.

SHOW ALL OF YOUR STEPS