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Discussion of Problem 1963. KiteThe problem is very easy. If you solved every geometry problem up to this one you should be able to solve it easily, so you might want to stop reading this. The axis of symmetry can be drawn in 2 places: through a pair of opposite point or through a pair of midpoints of opposite segments. Why only the midpoints? Because when you "fold" the figure your points must go one ever the other. If the distance is not equal, this is impossible(hint 1). M A N __.__ | \ \ | \ \ |___\__\ B M is the top-left point N is the top-right point This figure for example. A and B are the midpoints. But this is clearly not an axis of symmetry. After the folding, the top-left point will go above the top-right point. After the folding, the angle relative to the axis of symmetry will be the same. This is a midpoint. The angle with the center in A for example must have 180 degrees; angle(MAB) + angle(NAB) = 180 angle(MAB) = angle(NAB) x + x = 180 x = 90 It is now clear that the vector MN must be perpendicular on the vector AB(hint 2) I think this is more that enough for you to solve the problem/ Good luck! Edited by author 27.05.2018 15:16 Edited by author 27.05.2018 15:17 0 0 5 0 6 1 1 1 Answer: 0 My solution gives right answer on this test, but I still WA on test #4 :( Fixed, now WA 7. PS. Forget it, it was fail of my code. Now AC. Edited by author 04.05.2015 02:54 Edited by author 04.05.2015 16:49 x first or y first matters!!! Edited by author 06.07.2014 16:48 Give me test . please! I had troubles with this problem when used fractional arithmetic instead of integer one (WA #32). Maybe this could help. Not pretty sure, but maybe "trapeze". 0 0 2 2 8 2 10 0 Answer: 2 Edited by author 26.06.2013 15:28 thanks. I have known my mistake . Really my mistake is in trapeze ...! |
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