How Many Squares

[am.harel]

The question reads:
A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?

I understand the point in the explanation that because the sides have to have 10 length, you can figure out Pythagorean triplets that would create several squares. The explanation says to count all the possible combinations of 0 and 10, and 6 and 8, in all quadrants, to figure out how many possible squares. However, wouldn't points such as (6,8) and (6,-8) correspond to the same square, thus double counting certain possible squares? Hope you can clarify- if I have done a bad job explaining my issue please refer to the explanation on the CAT exam to get a better understanding.

[tim]

no, those are different squares. try drawing them and you'll see. you can't have a square with one vertex at the origin if it also has both (6,8) and (6,-8)..