Assignment 4: Centroid

by Butila Kialeuka(Diekumpuna)

__Constructing the Centroid__.

This is a geometric concept that entails constructing a
median, the middle point of the center of a segment that is equidistant, in
each given segment of the triangle. From the midpoint, there is a segment then constructed
that directly connects from the opposite vertex of the addressed segment;
consequently, all three newly created segments then intersect at the middle of
the triangle.

In a classroom setting, students will be introduced to what
is the centroid of a triangle and how to sketch on the geometry sketch pad.
Students will examine the relationships of the median of the given segments in
a triangle and how it directly relates to the centroid of the triangle.
Students will discover that the centroid is a point of concurrency in a
triangle as there are three intersecting lines constructed from each given
median of the triangle.

Students will explore
and conclude that distance from the centroid to the median of each respect
segment of the triangle is 2/3 of the segment connecting from the median to the
opposite vertex. Students will manipulate the sketch pad and add grid in order
to localize points of each segments.

Students will use the formula to calculate the midpoint
algebraically and compare it to the given coordinates of the sketch on the
sketchpad, m = (x_{1} +x_{2})/2, (y_{1}+y_{2})/2.
In addition, students will explore the distance formula of square root [(x_{2}-x_{1})^{2}
+ (y_{2}-y_{1})^{2}]. With the distance formula, we
will be able to prove that the centroid is indeed 2/3 the distance from the
vertex to the midpoint of the opposite vertex.

Students should thoroughly enjoy this assignment as they are
exploring the measuring geometrically and algebraically. Students should be
able to demonstrate the distance from centroid to the
selected vertex, using the distance formula equates 2/3 of the segment from the
midpoint to the opposite vertex.