you need to clarify this question. Are the triangles to be formed only with the given points as vertices? (i.e., are all of the sides of each triangle a complete segment from one point to another point?).
If so, i believe the answer is fairly straightforward....
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993