Centroid of A Triangle

Defined with examples and pictures

Definition

of the Centroid of a Triangle

The Centroid is a point of concurrency of the triangle. It is the point where all 3 medians intersect and is often described as the triangle's center of gravity or as the barycent.

Properties of the Centroid
Picture of Centroid of an Acute Triangle Picture of Centoid of a Triangle
Picture of Centroid of an Obtuse Triangle Centroid of Obtuse Triangle

Pictures of the 2:1 ratios formed by centroid and medians

Picture of Centroid Ratios Picture of Centroid Ratios 2 Picture of Centroid Ratios 3

Practice Problems

Problem 1

Point A is a midpoint and Point B is the centroid of the triangle pictured below, if the length of BC is 12, what is the length of AB ? You may assume the picture is drawn to scale.

Centroid Ratio Problem 1

To solve tis problem, just remember that the centroid divides each median in a 2 : 1 ratio. Therefore, we can use this ratio to solve for the length of AB as follows:

Problem 1

Point A is a midpoint and Point B is the centroid of the triangle pictured below, if the length of AB is 7, what is the length of BC ? You may assume the picture is drawn to scale.

Centroid Ratio Problem 2

To solve tis problem, just remember that the centroid divides each median in a 2 : 1 ratio. Therefore, we can use this ratio to solve for the length of AB as follows:

Ultimate Math Solver (Free)

Free Algebra Solver ... type anything in there!