How to Find the Centroid of a Triangle

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  • 0:04 The Centroid of a Triangle
  • 1:11 Final Solution
  • 1:21 Check Your Work
  • 2:13 Example Without Graphing
  • 3:13 Lesson Summary
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Lesson Transcript
Instructor: Maria Airth

Maria has a Doctorate of Education and over 20 years of experience teaching psychology and math related courses at the university level.

The centroid of a triangle is its center-most point. This point is an equal distance from each corner (vertex) of the triangle. To find the centroid you find the average of the x and y values of the vertices.

The Centroid of a Triangle

The centroid of a triangle is the center point equidistant from all vertices.

The formula is: Where the centroid is O, Ox = (Ax + Bx + Cx)/3 and Oy = (Ay + By + Cy)/3

Find the centroid of this triangle:

Sample Question

Step 1: Identify the coordinates of each vertex in the triangle (often these will already be labelled). In this example, the vertices are: A (4, 5), B (20, 25), and C (30, 6).

Step 2: Add all the x values from the three vertices coordinates and divide by 3 to get the x value of the centroid coordinate: 4 + 20 + 30 = 54/3 = 18

Step 3: Add all the y values from the three vertices coordinates and divide by 3 to get the y value of the centroid coordinate: 5 + 25 + 6 = 36/3 = 12

Step 4: Determine the centroid coordinate based on values found from the previous calculations: (18, 12).

Final Solution

The final solution could be given as the simple coordinate (18,12) or you could draw the centroid in the graph to illustrate its central position to the vertices.

Centroid of a Triangle

Check Your Work

A great way to check your work quickly is to actually graph the centroid coordinate to ensure that it appears in the center of the triangle. If this is not possible due to lack of accuracy in drawing or time constrictions, you can still check your work quickly.

Quickly review your x values: 4, 20, and 30. Is your centroid x value within this range? Would you guess that your centroid x value is about the average of these vertices x values? In fact, the centroid value is the exact average of the three corner points.

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