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.

https://latex.artofproblemsolving.com/b/c/3/bc36d6a86ebdd87399c8b07d66ec053e8593c264.png

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)

(a)

Let D, E, F be the midpoints of $\overline{BC},$ , \overline{AC},$ and $\overline{AB},$ 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.

Guest Mar 21, 2021