Question 1172342
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Answer: 5


This diagram shows all the possible squares.
<img src = "https://i.imgur.com/VeOHxwP.png">
The five possbile squares are
Square PABC (blue)
Square PCDE (blue)
Square PEFG (blue)
Square PHCJ (red) 
Square PJEK (red) 


The blue squares are all have side lengths of 2 units. The red squares have side lengths of sqrt(2) units. 


Note how P is 1 unit above the x axis. Reflecting it over the x axis leads to point C. We can see that segment PC is 2 units long. So that explains why square PABC is 2 by 2, and only one such square is possible where P(-1,1) is in the upper right corner and the sides are vertical. Similar logic applies to the other 2 blue squares. 


For the red squares, note how the axis of symmetry lies along the diagonals. If you reflect point E over the y axis, you arrive at point E. Points P and E are sufficient to form square PJEK, where P and E are opposite vertices. So only one red square is possible in this configuration. The other red square PHCJ is a similar story.
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