Question

在平面直角坐標(biāo)系中，正方形ABCD的頂點(diǎn)坐標(biāo)分別為A(1,1)，B(1,－1)，C(－1,－1)，D(－1,1)，y軸上有一點(diǎn)P(0,2)．作點(diǎn)P關(guān)于點(diǎn)A的對(duì)稱點(diǎn)P₁，作點(diǎn)P₁關(guān)于點(diǎn)B的對(duì)稱點(diǎn) P₂，作點(diǎn)P₂關(guān)于點(diǎn)C的對(duì)稱點(diǎn)P₃，作點(diǎn)P₃關(guān)于點(diǎn)D的對(duì)稱點(diǎn)P₄，作點(diǎn)P₄關(guān)于點(diǎn)A的對(duì)稱點(diǎn)P₅，作點(diǎn)P₅關(guān)于點(diǎn)B的對(duì)稱點(diǎn)P₆，…，按此操作下去，則點(diǎn)P₂₀₁₃的坐標(biāo)為       .

Answer 1

(2,0)

如圖,點(diǎn)P關(guān)于點(diǎn)A的對(duì)稱點(diǎn)P₁(2,0), 點(diǎn)P₁關(guān)于點(diǎn)B的對(duì)稱點(diǎn) P₂(0,-2), 點(diǎn)P₂關(guān)于點(diǎn)C的對(duì)稱點(diǎn)P₃(-2,0), 點(diǎn)P₃關(guān)于點(diǎn)D的對(duì)稱點(diǎn)P₄(0,2), P₄與P重合, P₅與P₁重合,故對(duì)稱點(diǎn)以4為一個(gè)循環(huán), P₁(2,0), P₂(0,-2), P₃(-2,0), P₄(0,2),2013除以4余1,所以P₂₀₁₃與P₁重合,故P₂₀₁₃(2,0).

試題分析：先求出幾個(gè)對(duì)稱點(diǎn)的坐標(biāo),然后找規(guī)律,由題,如圖,點(diǎn)P關(guān)于點(diǎn)A的對(duì)稱點(diǎn)P₁(2,0), 點(diǎn)P₁關(guān)于點(diǎn)B的對(duì)稱點(diǎn) P₂(0,-2), 點(diǎn)P₂關(guān)于點(diǎn)C的對(duì)稱點(diǎn)P₃(-2,0), 點(diǎn)P₃關(guān)于點(diǎn)D的對(duì)稱點(diǎn)P₄(0,2), P₄與P重合, P₅與P₁重合,故對(duì)稱點(diǎn)以4為一個(gè)循環(huán), P₁(2,0), P₂(0,-2), P₃(-2,0), P₄(0,2),2013除以4余1,所以P₂₀₁₃與P₁重合,故P₂₀₁₃(2,0).