(2005•南京)如果將點(diǎn)P繞定點(diǎn)M旋轉(zhuǎn)180°后與點(diǎn)Q重合,那么稱點(diǎn)P與點(diǎn)Q關(guān)于點(diǎn)M對(duì)稱,定點(diǎn)M叫做對(duì)稱中心.此時(shí),M是線段PQ的中點(diǎn).如圖,在直角坐標(biāo)系中,△ABO的頂點(diǎn)A,B,O的坐標(biāo)分別為(1,0),(0,1),(0,0).點(diǎn)列P
1,P
2,P
3,…中的相鄰兩點(diǎn)都關(guān)于△ABO的一個(gè)頂點(diǎn)對(duì)稱:點(diǎn)P
1與點(diǎn)P
2關(guān)于點(diǎn)A對(duì)稱,點(diǎn)P
2與點(diǎn)P
3關(guān)于點(diǎn)B對(duì)稱,點(diǎn)P
3與點(diǎn)P
4關(guān)于點(diǎn)O對(duì)稱,點(diǎn)P
4與點(diǎn)P
5關(guān)于點(diǎn)A對(duì)稱,點(diǎn)P
5與點(diǎn)P
6關(guān)于點(diǎn)B對(duì)稱,點(diǎn)P
6與點(diǎn)P
7關(guān)于點(diǎn)O對(duì)稱…對(duì)稱中心分別是A,B,O,A,B,O,…,且這些對(duì)稱中心依次循環(huán).已知點(diǎn)P
1的坐標(biāo)是(1,1),那么P
2的坐標(biāo)是
(1,-1)
(1,-1)
,P
7的坐標(biāo)是
(1,1)
(1,1)
,P
100的坐標(biāo)是
(1,-3)
(1,-3)
.