SOLUTION: Three vertices of a quadrilateral are (-1,-1), (1,2), and (5,-1). What are the coordinates of two vertices that will form two different parallelograms?

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