在平面直角坐標(biāo)系中,O為原點(diǎn),點(diǎn)A(3,0),點(diǎn)B(0,4),把△ABO繞點(diǎn)A順時(shí)針旋轉(zhuǎn),得△AB′O′,點(diǎn)B,O旋轉(zhuǎn)后的對(duì)應(yīng)點(diǎn)為B′,O.
(Ⅰ)如圖①,當(dāng)旋轉(zhuǎn)角為90°時(shí),求BB′的長(zhǎng);
(Ⅱ)如圖②,當(dāng)旋轉(zhuǎn)角為120°時(shí),求點(diǎn)O′的坐標(biāo);
(Ⅲ)在(Ⅱ)的條件下,邊OB上的一點(diǎn)P旋轉(zhuǎn)后的對(duì)應(yīng)點(diǎn)為P′,當(dāng)O′P+AP′取得最小值時(shí),求點(diǎn)P′的坐標(biāo).(直接寫出結(jié)果即可)