Given the coordinates of the three vertices of a triangle ABC,

the centroid O coordinates are given by
where A_{x} and A_{y} are the x and y coordinates of the point A etc..

the centroid O coordinates are given by

Try this
Drag any point A,B,C. The centroid O of the triangle ABC is continuously recalculated using the above formula.
You can also drag the origin point at (0,0).

Recall that the centroid of a triangle is the point where the triangle's three medians intersect. It is also the center of gravity of the triangle. For more see Centroid of a triangle.

The coordinates of the centroid are simply the average of the coordinates of the vertices. So to find the x coordinate of the orthocenter, add up the three vertex x coordinates and divide by three. Repeat for the y coordinate.

x | y | |

A | ||

B | ||

C | ||

Centroid | ||

Use the calculator to calculate coordinates of the centroid of the triangle ABC. Enter the x,y coordinates of each vertex, in any order.

- In the diagram at the top of the page, Drag the points A, B or C around and notice how the centroid moves and the coordinates are calculated. Try points that are negative in x and y. You can drag the origin point to move the axes.
- Click "hide details". Drag the triangle to some random new shape. Calculate the centroid position then click "show details" to see if you got it right.

In the interest of clarity in the applet above, the coordinates are rounded off to integers. This can cause calculations to be slightly off.

For more see Teaching Notes

- Introduction to coordinate geometry
- The coordinate plane
- The origin of the plane
- Axis definition
- Coordinates of a point
- Distance between two points

- Introduction to Lines

in Coordinate Geometry - Line (Coordinate Geometry)
- Ray (Coordinate Geometry)
- Segment (Coordinate Geometry)
- Midpoint Theorem

- Cirumscribed rectangle (bounding box)
- Area of a triangle (formula method)
- Area of a triangle (box method)
- Centroid of a triangle
- Incenter of a triangle
- Area of a polygon
- Algorithm to find the area of a polygon
- Area of a polygon (calculator)
- Rectangle
- Square
- Trapezoid
- Parallelogram

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