*I*don't even know how we're gonna prove this thing. We learned from the midsegment theorem that defining the vertices using (x

_{1}, y

_{1}), (x

_{2}, y

_{2}), (x

_{3}, y

_{3}) helped out greatly. So, what the heck, let's try it again.

We know we can define the midpoints generally as well, so that's what we do. Then it hits! We can define the vector from the vertex to the midtpoint of the opposite side, use a scalar of 2/3 to determine the vector from the vertex to what's supposed to be the centroid and then translate the vertex to said point.

**Ta-freakin'-da**

Turns out that the centroid is 1/3(x

_{1}+ x

_{2}+x

_{3}, y

_{1}+ y

_{2}+y

_{3}).

I didn't know that. If this is what it's like to become a co-learner with your students, then sign me the heck up.

Cool. And then afterwards, did you make him cut out a triangle, draw its medians/centroid, and then test to see if the centroid really is the balance point?

ReplyDeleteMy kids LOVE centroids, because you can kinesthetically verify their significance.