Parallelogram fourth corner

[zeion]

1. The problem statement, all variables and given/known data

If three corners of a parallelogram are (1,1), (4,2), and (1,3), what are all the possible fourth corners?


2. Relevant equations



3. The attempt at a solution

The only possible fourth corner is (4,4) if the other 3 points are set.
The solution says (4,0) and (-2,2) can also be corners. How is this possible

[symbolipoint]

Take the problem description to a graph of the points given, and literally test the answer key solution visually; is it also a vertex of a parallelogram? Now, if so, how can you account for this symbolically?

[zgozvrm]

Note that given 3 non-collinear points A, B, & C, you can create a triangle [itex]\triangle[/tex]ABC

A parallelogram, when divided along one of its diagonals, results in two identical triangles rotated 180[itex]^\circ[/tex] with respect to each other.
So, any triangle can describe 3 parallelograms.