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本文更新于洛谷的博客。

题目描述

给定平面直角坐标系中的四个点,画一个正方形,使这(4)个点在正方形各边的直线上。

题解

补充三元_树的证明好像挺简单的。

wysr0xfsxym2651.png

over \(A \)as \(AM \ perp BS \)as \(BS \)as \(M \),over \(C \)as \(CN \ perp DX \)as \(DX \)as \(N \)

\(\因为AP\perp DX,BQ\perp DX\)

\(\因此AP\parallel BQ\)

\(\(\因为RS \并行PQ\ \)

\(\(\因此\)四边形\(PQSR\)是长方形。

\(\因为\角度BKX=\角度BQX=90 \度\)

\(\因此\角度CXN=\角度ABM\)

\ (\因为\ anglecnx=\ angleamb=90 \度,CX=ab \)

\(\因此\三角形cong \丛\三角形ABM(AAS)\)

\(\因此CN=AM\)

\(\因此PR=QS=CN=AM=PQ=RS\)

\(\(\因此\)四边形\(PQSR\)是正方形。

由于\(C\)和\(AB\)的相对位置,可能会改变\(PQRS\)的顺序,但这没有影响。

注意输出的顺序就行了。

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