Centroid: Definition, Formula & Solved Problems

Centroid: Centroid is a center point of an object. In case of triangle, all the three median intersect at a common point known as centroid. It is calculated by taking x and y coordinates of triangles. Centroid is the center of gravity present inside the object. According to the centroid theorem, the centroid is present at 2/3rd of the distance from the vertex to the mid points of the sides.

This is the most important concept in geometry. Students learn centroid in their primary classes in order to solve mathematical problems quickly. You can check NCERT Solutions for Class 10 Maths Chapter 10 for better understanding. We have provided detailed information on centroid in this article. Read on to find out about its definition, formula and solved examples.

Centroid Definition

Centroid is the center position of an object. For example, when all the three median intersect at the common point in a triangle is called as centroid of triangle. It is present in inside the object. The median is a line segment that joins the midpoint of triangle. We can say that, the triangle is divided into the ratio 2:1.

According to the centroid theorem, it is located at the 2/3rd of the distance away from the vertex to the midpoints of the sides. Let us consider triangle ABC, where D,E,F, and G are the midpoints of the side AB,BC and CA respectively, Hence as per the theorem, BG=2/3 BF, CG=2/3CD and AG=2/3 DE.

Properties of centroid

It is located inside the object.
It is the center point of the object
It is the point where all the medians meet.

Formula Of Centroid

Consider a triangle ABC, whose vertices are A(x₁, y₁), B(x₂, y₂), C(x₃, y₃), Thus, the centroid is calculated by taking the average of all the three vertices by using the formula as mentioned below:

Centroid of a triangle = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3)

Examples Of Centroid

Some of the examples of centroid are given below:

Example 1: Find the centroid of the triangle whose vertices are A (4, 8), B(3, 9), and C(5,10).

Solution: Given, A(x₁, y₁) = A(4, 8), B(x₂, y₂) = B(3,9) and C(x₃, y₃) = C(5,10)

Centroid of a triangle = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3)

Centroid of a triangle = ((4+3+5)/3, (8+9+10)/3)

= (12/3, 27/3)

= (4, 9)

Therefore, the centroid of the triangle for the given vertices is (4, 9).

Example 2: Find the centroid of the triangle whose vertices are A (8, 16), B(9, 18), and C(7,14).

Solution: Given, A(x₁, y₁) = A(8, 16), B(x₂, y₂) = B(9,18) and C(x₃, y₃) = C(7,14)

Centroid of a triangle = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3)

Centroid of a triangle = ((8+9+7)/3, (16+18+14)/3)

= (24/3, 48/3)

= (8, 16)

Therefore, the centroid of the triangle for the given vertices is (8, 16) .

Download NCERT Solutions for Class 10 Maths Chapter 7 PDF

FAQs On Centroid

The frequently asked questions on centroid are given below:

Q. What is centroid?
A. Centroid is an center point of an object.

Practice 12th CBSE Exam Questions

Q. What is the formula of centroid?
A. The formula used to calculate centroid is ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3)

Q. What is the theorem of centroid?
A. According to the centroid theorem, the centroid is present at 2/3rd of the distance from the vertex.

Q. What are the properties of centroid?
A. The properties of centroid are as follows:
1. It is located inside the object.
2. It is the center point of the object
3. It is the point where all the medians meet.

So, now you have all the information about the centroid in this article. Make the best use of them and crack your CBSE Class 10 board exam with good scores and choose the career you want for your future.

If you have any queries regarding Centroid, feel to leave a comment below. We will surely help you out.