The Other Two Trees

最新推荐文章于 2019-02-21 17:32:14 发布

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最新推荐文章于 2019-02-21 17:32:14 发布

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分类专栏： UVA 基本数学问题

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基本数学问题

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本问题探讨了如何通过已知两个相对邻居的土地中心树的坐标来确定另外两个邻居的土地中心树坐标的方法。输入包含多组数据，每组数据为两个坐标，输出为另外两个坐标或Impossible。

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Problem E

The Other Two Trees

Input: standard input

Output: standard output

Time Limit: 2 seconds

You have a quadrilateral shaped land whose opposite fences are of equal length. You have four neighbors whose lands are exactly adjacent to your four fences, that means you have a common fence with all of them. For example if you have a fence of length d in one side, this fence of length d is also the fence of the adjacent neighbor on that side. The adjacent neighbors have no fence in common among themselves and their lands also don’t intersect. The main difference between their land and your land is that their lands are all square shaped. All your neighbors have a tree at the center of their lands. Given the Cartesian coordinates of trees of two opposite neighbors, you will have to find the Cartesian coordinates of the other two trees.

Input

The input file contains several lines of input. Each line contains four floating point or integer numbers x1, y1, x2, y2, where (x1, y1), (x2, y2) are the coordinates of the trees of two opposite neighbors. Input is terminated by end of file.

Output

For each line of input produce one line of output which contains the line “Impossible.” without the quotes, if you cannot determine the coordinates of the other two trees. Otherwise, print four floating point numbers separated by a single space with ten digits after the decimal pointax1, ay1, ax2, ay2, where (ax1, ay1) and (ax2, ay2) are the coordinates of the other two trees. The output will be checked with special judge program, so don’t worry about the ordering of the points or small precision errors. The sample output will make it clear.