manhattenGmat上碰到的一道题．．大家帮忙看下吧

在直角坐标系里，一个正方形的一个顶点在原点上，正方形的面积是100，问每个顶点的坐标都是整数的摆放方式有几种

谢谢各位啦~

由于正方形的一个顶点是原点，则设和原点相邻的定点为(a,b)，因为面积为100，则边长为10，那么a^2+b^2=100

则a和b的绝对是可以为（10,0),(0,10),(6,8)和（8,6)

再将正负号考虑在内的话，每个都有4种可能性，那么应该是12种情况

不知道我有否遗漏的情况在内，希望lz提供答案

不对，我考虑疏忽了，应该只有8种，(6,8)和(8,6)的情况是重合的

正确答案我也不知道，当时做完题目只能显示对错。

恩，应该是8种。。我刚才好好画了画~

呵呵，谢谢啦

en，请问manhattonGMAT是模考软件吗？

嗯，我是用邮箱注册的，一个邮箱可以免费模考一次

我也是看到论坛上别人说，我才去试试

不过好像不能看到答案和解释的是不是~

这道题做的时候很不确定，就有印象，所以想起来问一下

可以看答案和解释的，在results里面点view，再点每道题，就有详细解释。这道题我也做到了，解释如下，够详细吧！

Each side of the square must have a length of 10.  If each side were to be 6, 7, 8, or most other numbers, there could only be four possible squares drawn, because each side, in order to have integer coordinates, would have to be drawn on the x- or y-axis.  What makes a length of 10 different is that it could be the hypotenuse of a Pythagorean triple, meaning the vertices could have integer coordinates without lying on the x- or y-axis. 

For example, a square could be drawn with the coordinates (0,0), (6,8), (-2, 14) and (-8, 6).  (It is tedious and unnecessary to figure out all four coordinates for each square).

If we label the square abcd, with a at the origin and the letters representing points in a clockwise direction, we can get the number of possible squares by figuring out the number of unique ways ab can be drawn.

a has coordinates (0,0) and b could have the following coordinates, as shown in the picture:


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

There are 12 different ways to draw ab, and so there are 12 ways to draw abcd. 

The correct answer is E.

哦。。。我晕，没仔细看呐，那我一整套题都没有看正确答案~~

多谢多谢

牛X， 这题有点搞，比GMAT题难