__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.

First we start with three points

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

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