# Centroid of a Triangle

How to solve the centroid of a triangle problems: definition, properties, examples, and their solutions.

## Definition

The centroid of a triangle

is the balance point of the triangle.

By putting the centroid of the triangle

on the tip of a finger,

it'll be balanced.

So its coordinates

are the means of each triangle's vertex.

## Example 1

*M*(*x* value's mean, *y* value's mean)

## Properties

Three medians of a triangle

meet at the centriod.

The centroid divides each median

in the ratio of 2 : 1.

(purple) : (blue) = 2 : 1

## Example 2

Point *M* is the centroid.

So *AP* is the median of △*ABC*.

Then *BP* = *PC*.

5*y* + 11 = 6

Point *M*, the centroid, divides *AP*

in the ratio of 2 : 1.

(purple) : (blue) = 2 : 1

So 8 : 3*x* - 2 = 2 : 1.

Proportion