Q: 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?

OA 12.

According to the answer key a has coordinates (0,0) and b could have the following coordinates,

(-10,0)
(-8,6)
(-6,8)
(0,10)
(6,8)
(8,6)
(10,0)
(8, -6)
(6, -8)
(0, 10)
(-6, -8)
(-8, -6)

However, when doing the problem myself, I considered the coordinates (-8,6) and (-8,-6) to be a part of the SAME square. The same can be said of the other coordinates that are actually part of the same square. Using this logic, 8 of the "distinctive" squares that are mentioned are actually only 4. Therefore, I reasoned that 8 was the correct answer.

Any thoughts?