Question 990691
<pre>
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:

{{{drawing(400,250,-7,9,-6,4, grid(1),


circle(1,2,0.15),circle(1,2,0.13),circle(1,2,0.11),circle(1,2,0.09),circle(1,2,0.07),circle(1,2,0.05),circle(1,2,0.03),circle(1,2,0.01),

circle(-1,-1,0.15),circle(-1,-1,0.13),circle(-1,-1,0.11),circle(-1,-1,0.09),circle(-1,-1,0.07),circle(-1,-1,0.05),circle(-1,-1,0.03),circle(-1,-1,0.01),

circle(5,-1,0.15),circle(5,-1,0.13),circle(5,-1,0.11),circle(5,-1,0.09),circle(5,-1,0.07),circle(5,-1,0.05),circle(5,-1,0.03),circle(5,-1,0.01) )}}}


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:

{{{drawing(400,250,-7,9,-6,4, grid(1),

red(line(1,2,7,2),line(7,2,5,-1),line(5,-1,-1,-1),line(-1,-1,1,2),


circle(7,2,0.15),circle(7,2,0.13),circle(7,2,0.11),circle(7,2,0.09),circle(7,2,0.07),circle(7,2,0.05),circle(7,2,0.03),circle(7,2,0.01)

),

circle(1,2,0.15),circle(1,2,0.13),circle(1,2,0.11),circle(1,2,0.09),circle(1,2,0.07),circle(1,2,0.05),circle(1,2,0.03),circle(1,2,0.01),

circle(-1,-1,0.15),circle(-1,-1,0.13),circle(-1,-1,0.11),circle(-1,-1,0.09),circle(-1,-1,0.07),circle(-1,-1,0.05),circle(-1,-1,0.03),circle(-1,-1,0.01),

circle(5,-1,0.15),circle(5,-1,0.13),circle(5,-1,0.11),circle(5,-1,0.09),circle(5,-1,0.07),circle(5,-1,0.05),circle(5,-1,0.03),circle(5,-1,0.01) )}}}

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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:

{{{drawing(400,250,-7,9,-6,4, grid(1),

red(line(1,2,-5,2),line(-5,2,-1,-1),line(5,-1,-1,-1),line(5,-1,1,2),



circle(-5,2,0.15),circle(-5,2,0.13),circle(-5,2,0.11),circle(-5,2,0.09),circle(-5,2,0.07),circle(-5,2,0.05),circle(-5,2,0.03),circle(-5,2,0.01)



),

circle(1,2,0.15),circle(1,2,0.13),circle(1,2,0.11),circle(1,2,0.09),circle(1,2,0.07),circle(1,2,0.05),circle(1,2,0.03),circle(1,2,0.01),

circle(-1,-1,0.15),circle(-1,-1,0.13),circle(-1,-1,0.11),circle(-1,-1,0.09),circle(-1,-1,0.07),circle(-1,-1,0.05),circle(-1,-1,0.03),circle(-1,-1,0.01),

circle(5,-1,0.15),circle(5,-1,0.13),circle(5,-1,0.11),circle(5,-1,0.09),circle(5,-1,0.07),circle(5,-1,0.05),circle(5,-1,0.03),circle(5,-1,0.01) )}}}

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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:

{{{drawing(400,250,-7,9,-6,4, grid(1),

red(line(1,2,-1,-1),line(3,-4,-1,-1),line(5,-1,3,-4),line(5,-1,1,2),

circle(3,-4,0.15),circle(3,-4,0.13),circle(3,-4,0.11),circle(3,-4,0.09),circle(3,-4,0.07),circle(3,-4,0.05),circle(3,-4,0.03),circle(3,-4,0.01)





),

circle(1,2,0.15),circle(1,2,0.13),circle(1,2,0.11),circle(1,2,0.09),circle(1,2,0.07),circle(1,2,0.05),circle(1,2,0.03),circle(1,2,0.01),

circle(-1,-1,0.15),circle(-1,-1,0.13),circle(-1,-1,0.11),circle(-1,-1,0.09),circle(-1,-1,0.07),circle(-1,-1,0.05),circle(-1,-1,0.03),circle(-1,-1,0.01),

circle(5,-1,0.15),circle(5,-1,0.13),circle(5,-1,0.11),circle(5,-1,0.09),circle(5,-1,0.07),circle(5,-1,0.05),circle(5,-1,0.03),circle(5,-1,0.01) )}}}

Edwin</pre>