There are actually three verticies that will form different parallelograms,
with the given coordinates of vertices.  You are only asked for two of them.
Here are the points:




There is nothing to calculate in this problem. All you do is count units
on the graph horizontally and vertically.

First solution:

To go from (-1,-1) to (1,2) you must move right 2 units and up 3 units.
Therefore do the same, starting at (5,1). Go right 2 units and up 3 units.
That will put you at the point (7,2).  So here is that parallelogram:



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Second solution:

To go from (5,-1) to (1,2) you must move left 4 units and up 3 units.
Therefore do the same, starting at (-1,-1). Go left 4 units and up 3 units.
That will put you at the point (-5,2).  So here is that parallelogram:



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Third solution:

To go from (1,2) to (-1,-1) you must move left 2 units and down 3 units.
Therefore do the same, starting at (5,-1). Go left 2 units and down 3 units.
That will put you at the point (3,-4).  So here is that parallelogram:



Edwin