如果將點(diǎn)P繞定點(diǎn)M繞轉(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).
(1)如果,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.
(2)點(diǎn)P
3與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)稱中心分別為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),則點(diǎn)P
2的坐標(biāo)為
,點(diǎn)P
100的坐標(biāo)為
.