Centroid of a triangle definition and formula explained

Learn and know about the centroid of a triangle. Centroid is one of the most important topics one should study in coordinate geometry chapter. So now we will learn the actual meaning of the centroid and also we will learn how we can find the centroid. 

Centroid of a triangle

First, we will see the definition of the centroid and after that, we will see properties of centroid, formula and representation of centroid for different kinds of triangle one by one.

Definition of the centroid of a triangle:

The intersection point of all the three medians of a triangle is called centroid. Centroid is represented with the letter G.

Centroid of a triangle

In the above triangle, we can observe three medians i.e. AD, BE and CF. we can also observe that all the three medians are meeting at one point, that point we are going to call as the centroid ( G).

Important Property of a centroid:

We should know that centroid (G ) divides the medians in 2: 1 ratio.

The Formula for finding the centroid of a triangle with vertices:

Suppose If A ( x1 , y1) , B ( x2, y2) C( x3, y3) are the given three vertices of a triangle then centroid is given by

Centroid of a triangle

Problems based on the centroid:

Find the centroid of triangle with vertices A (1, 5), B (2, 7) and C (6, 3).

Solution:

Centroid of a triangle

In a Δ ABC, the centroid is (7, 2) and the two vertices of the triangle are given by (1, 8), (10, 4) then find the third vertex of a triangle.

Solution:

Let the two vertices of a triangle be A (1, 8), B (10, 4) and the third vertex be C (x, y).

Centroid of a triangle

Representation of centroid for right, acute and obtuse angled triangles:

Centroid of a triangle

Centroid of a triangle

Centroid of a triangle

I hope you learnt everything about the centroid i.e. definition, formula and property.

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