Why do this problem?
Learners can investigate using the interactivity, make a conjecture
and then try to prove their own conjecture.
It can be an exercise in coordinates.
It is useful for learners to appreciate that the symmetry of the
result makes it unecessaryto work out all three distances.
Ideally learners would work independently on this problem.
How do we find the coordinates of the centroid of an equilateral
educational mathematics software and your learners can experiment
with it and draw their own dynamic diagrams.