Possible Fourth Corners of a Parallelogram Given Three Non-Collinear Points

[zeion]

Homework Statement

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

Homework Equations

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