CENTROID
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.
Video Examples: Centroid
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 onCentroid
Ques: Find the coordinates of the centroid of â–³XYZ 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 the X-coordinates and the mean of the Y-coordinates of the triangle's vertices.
Step 2: The mean of the X-coordinates is (- 4 + 0 + 3)/3 = - 1/3.
Step 3: The mean of the Y-coordinates is (2 + 5 + (- 1))/3 = 2.
Step 4: The coordinates of the centroid is (- 1/3, 2).
Quick Summary
- The centroid is the intersection point of a triangle's medians.
- The centroid divides each median in a 2:1 ratio.
🍎 Teacher Insights
Emphasize the difference between the centroid and other triangle centers. Use physical models to demonstrate the center of mass concept.🎓 Prerequisites
- Coordinates Geometry
- Medians of a triangle
- Basic Algebra
Check Your Knowledge
Q1: The vertices of a triangle are (0,0), (6,0), and (0,9). What are the coordinates of the centroid?
Q2: If a median of a triangle has a length of 9 units, what is the distance from the vertex to the centroid?
Frequently Asked Questions
Q: How do you find the centroid of a triangle?
A: The centroid is found by averaging the x-coordinates and the y-coordinates of the three vertices.
Q: What is the ratio in which the centroid divides the median?
A: The centroid divides the median in the ratio 2:1.