如圖,在平面直角坐標(biāo)系中,菱形ABOC的頂點(diǎn)A在x軸上,頂點(diǎn)B在反比例函數(shù)
y=(x>0)的圖象上.當(dāng)菱形的頂點(diǎn)A在x的正半軸上自左向右移動(dòng)時(shí),頂點(diǎn)B也隨之在反比例函數(shù)
y=(x>0)的圖象上滑動(dòng),點(diǎn)C也相應(yīng)移動(dòng),但頂點(diǎn)O始終在原點(diǎn)不動(dòng).
(1)如圖①,若點(diǎn)A的坐標(biāo)為(6,0)時(shí),求點(diǎn)B、C的坐標(biāo);
(2)如圖②,當(dāng)點(diǎn)A移動(dòng)到什么位置時(shí),菱形ABOC變成正方形,請(qǐng)說(shuō)明理由;
(3)當(dāng)菱形的三個(gè)頂點(diǎn)在作上述移動(dòng)時(shí),菱形ABOC的面積是否會(huì)發(fā)生變化,若不發(fā)生變化,請(qǐng)求出菱形的面積;若發(fā)生變化,請(qǐng)說(shuō)明變化的規(guī)律.