The length of the diagonal with coordinates (x, y) of the square is = √ (10²+10²) = 10√2
So its distance from (0,0) is √{(x-0)²+√ (y-0)²} =10√ 2
or x²+y²= 200
just the knowledge that this represents a circle is enough. So any point on the circle is valid.

For clarity the circle has a centre at origin and the diagonal of the square is the radius = 10√ 2

OA I for Infinite

righty123 wrote: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?

In order to maintain the condition that the coordinates of all vertices are integers, only those squares, which include the pair of coordinate axes as one pair of consecutive sides, can be counted. My answer to the question is [spoiler]4[/spoiler].

Can someone please explain the logic behind this!!