**Definition of Centroid**

- Centroid of a triangle is the point of intersection of all its three medians.
- The centre of mass of a uniform object is also called as Centroid.

**More about Centroid**

- The centroid of a triangle divides the medians in the ratio 2:1.

**Example of Centroid**

- In the above triangle, AL, BM, CN are the medians of the triangle and they intersect at the point P. So, the point P is the centroid of the triangle.

**Solved Example on Centroid**

Find the coordinates of the centroid of ΔXYZ with X (- 4, 2), Y (0, 5), and Z (3, - 1).

Choices:

A. (- 1/3, 2)

B. (1/3, 2)

C. (- 1/3, - 2)

D. (- 1/3, - 1/2)

Correct Answer: A

Solution:

Step 1:The centroid of a triangle is the mean of theX-coordinates and the mean of theY-coordinates of the triangle's vertices.

Step 2:The mean of theX-coordinates is (- 4 + 0 + 3)/3 = - 1/3.

Step 3:The mean of theY-coordinates is (2 + 5 + (- 1))/3 = 2.

Step 4:The coordinates of the centroid is (- 1/3, 2).

**Related Terms for Centroid**

- Mean
- Median
- Point of Intersection
- Triangle
- Vertices