How this calculator works
The centroid is the average of the three vertices and the intersection of the medians. Each median joins a vertex to the opposite side midpoint. The centroid lies two thirds of the way from the vertex along that median. Reversing the coordinate average recovers a missing vertex, after which the calculator verifies that the triangle has positive area.
Formula
G=(A+B+C)/3; C=3G-A-B. For opposite midpoint M: AG=2AM/3 and GM=AM/3.
Worked example
Vertices (0,0), (6,0), (0,6) have centroid (2,2). The median from the origin ends at (3,3), has length 3√2, and divides into 2√2 and √2. If G=(2,4), A=(1,2) and B=(4,2), the missing vertex is C=(1,8).
Advertisement
Frequently asked questions
Is this the centre of the circumcircle?
No. The centroid averages vertices and balances a uniform triangular sheet. The circumcentre is equally distant from all three vertices.
Which vertex can be recovered?
Label the missing vertex C and enter the two known vertices as A and B. Relabelling does not change the centroid.
Can a centroid lie outside a triangle?
For a genuine triangle it always lies inside. A result outside your drawn outline suggests that coordinates or labels were entered incorrectly.