Centroid of a Triangle Calculator

What is the Centroid of a Triangle?

Imagine you have a triangle-shaped cookie, and you want to balance it on the tip of your finger. The centroid is the special point where your cookie would balance perfectly! It's like the triangle's center of gravity.

How to Calculate the Centroid of a Triangle

Finding the centroid is like solving a fun puzzle. We use the coordinates of the triangle's corners to figure out where this special balancing point is. It's similar to finding the middle of the triangle, but with a twist!

Formula

The magical formula for finding the centroid of a triangle with corners (x₁, y₁), (x₂, y₂), and (x₃, y₃) is:

\[ C_x = \frac{x_1 + x_2 + x_3}{3}, \quad C_y = \frac{y_1 + y_2 + y_3}{3} \]

Where:

• \(C_x\) is the x-coordinate of the centroid
• \(C_y\) is the y-coordinate of the centroid
• \(x_1, x_2, x_3\) are the x-coordinates of the triangle's corners
• \(y_1, y_2, y_3\) are the y-coordinates of the triangle's corners

Calculation Steps

1. Write down the coordinates of your triangle's corners
2. Add up all the x-coordinates and divide by 3
3. Add up all the y-coordinates and divide by 3
4. The results are your centroid's coordinates!

Example and Visual Representation

Let's find the centroid of a triangle with corners at (0, 0), (6, 0), and (3, 4):

• \(C_x = \frac{0 + 6 + 3}{3} = 3\)
• \(C_y = \frac{0 + 0 + 4}{3} = \frac{4}{3} \approx 1.33\)

So, the centroid is at (3, 1.33). Here's what this triangle and its centroid look like:

In this picture, you can see our blue triangle. The red dot is the centroid, right where all three dashed lines (called medians) meet. It's like the triangle's perfect balancing point!