Where is the centroid?

By Brandie Thrasher

When asked, most students would probably say that they had never heard of a centroid in their many years of math. So, this means that they probably wouldnÕt know how to locate it, as if it happened to be lost!

First, what is a centroid? A centroid is the point where the three medians of the triangle intersect.  It is also referred to as the center of gravity of a triangle, or one of a triangleÕs points of concurrency. Well, what is a median of a triangle? A triangle has three medians; each median is a line that connects a vertex to a midpoint on a segment that is opposite the vertex.

Now that we have a little background information, letÕs construct a triangle and find its centroid.

Connect the points with segments and we have a triangle.

The midpoint of a line segment divides the segment into two equal parts.  When measured, here are the midpoints of the triangle.

As stated earlier, we must connect each midpoint to the vertex opposite to it, as shown here

The point at which all three segments intersect is called the centroid.

Lets take a look at some various centroids.

No matter the shape or size of a triangle, it will always carry this property!!

See a triangle in motion, and see its centroid here!

Reference:

http://www.mathopenref.com/trianglecentroid.html