My thoughts

1. None of the dots can be at corner, since 2 dots cannot cover size 5 triangle.

2. We need one dot on every edge. Suppose there was no dot on the bottom edge, each dot can color 2 cells on the edge. 3 dots can cover 6 cells. But there are 7 cells on the edge.

3. Rotate triangle by 120 degrees and you get the same. So the solution is most likely symmetric.