Question

如圖,點(diǎn)O（0,0）、B（0,1）是正方形OBB₁C的兩個(gè)頂點(diǎn),以對(duì)角線OB₁為一邊作正方形OB₁B₂C₁,再以正方形OB₁B₂C₁的對(duì)角線OB₂為一邊作正方形OB₂B₃C₂,…,依次下去,則點(diǎn)B₂₀₁₄的坐標(biāo)是      .

Answer 1

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試題分析：根據(jù)題意和圖形可看出每經(jīng)過一次變化,都順時(shí)針旋轉(zhuǎn)45°,邊長都乘以,所以B₁(1,1)、B₂(2,0)、B₃(2,-2)、B₄(0,-4)、B₅(-4,-4)、B₆(-8,0)、B₇( ,8)、B₈(0,16)、B₉(16,16)的坐標(biāo),由規(guī)律可以發(fā)現(xiàn),每經(jīng)過8次作圖后,點(diǎn)的坐標(biāo)符號(hào)與第一次坐標(biāo)符號(hào)相同,每次正方形的邊長變?yōu)樵瓉淼?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823031701146344.png" style="vertical-align:middle;" /> 倍,
,2014÷8="251…6," B₂₀₁₄的縱橫坐標(biāo)符號(hào)與點(diǎn)B₆的相同,橫坐標(biāo)是負(fù)值,縱坐標(biāo)為0,然后根據(jù)規(guī)律計(jì)算出點(diǎn)B₂₀₁₄的坐標(biāo) ．
故答案是．