我們將數(shù)軸上點(diǎn)P表示的數(shù)記為x
P.對(duì)于數(shù)軸上不同的三個(gè)點(diǎn)M,N,T,若有x
N-x
T=k(x
M-x
T),其中k為有理數(shù),則稱點(diǎn)N是點(diǎn)M關(guān)于點(diǎn)T的“k星點(diǎn)”.已知在數(shù)軸上,原點(diǎn)為O,點(diǎn)A,點(diǎn)B表示的數(shù)分別為x
A=-2,x
B=3.
(1)若點(diǎn)B是點(diǎn)A關(guān)于原點(diǎn)O的“k星點(diǎn)”,則k=
;若點(diǎn)C是點(diǎn)A關(guān)于點(diǎn)B的“2星點(diǎn)”,則x
c=
-7
-7
;
(2)若點(diǎn)D表示的數(shù)為x
D=5,且點(diǎn)A、D均以每秒1個(gè)單位長(zhǎng)度沿正方向運(yùn)動(dòng).是否存在某一時(shí)刻,使得點(diǎn)D是點(diǎn)A關(guān)于點(diǎn)O的“-2星點(diǎn)”?若存在,求出運(yùn)動(dòng)時(shí)間;若不存在,請(qǐng)說(shuō)明理由;
(3)點(diǎn)Q在數(shù)軸上運(yùn)動(dòng)(點(diǎn)Q不與A,B兩點(diǎn)重合),作點(diǎn)A關(guān)于點(diǎn)Q的“2星點(diǎn)”,記為A′,作點(diǎn)B關(guān)于點(diǎn)Q的“2星點(diǎn)”,記為B′.當(dāng)點(diǎn)Q運(yùn)動(dòng)時(shí),QA′+QB′是否存在最小值?若存在,求出最小值及相應(yīng)點(diǎn)Q的位置;若不存在,請(qǐng)說(shuō)明理由.