點(diǎn)M(2,-3,1)關(guān)于坐標(biāo)原點(diǎn)對(duì)稱的點(diǎn)是( )
A.(-2,3,-1)
B.(-2,-3,-1)
C.(2,-3,-1)
D.(-2,3,1)
【答案】分析:根據(jù)空間直角坐標(biāo)系中兩個(gè)關(guān)于原點(diǎn)的對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn):“關(guān)于原點(diǎn)對(duì)稱的點(diǎn),橫坐標(biāo)、縱坐標(biāo)、豎坐標(biāo)都互為相反數(shù)”進(jìn)行解答.
解答:解:由空間直角坐標(biāo)系中關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)特點(diǎn):
橫坐標(biāo)、縱坐標(biāo)、豎坐標(biāo)都互為相反數(shù),
可得點(diǎn)P(2,-3,1)關(guān)于坐標(biāo)原點(diǎn)的對(duì)稱點(diǎn)的坐標(biāo)為(-2,3,-1),
故選A.
點(diǎn)評(píng):解決本題的關(guān)鍵是掌握好對(duì)稱點(diǎn)的坐標(biāo)規(guī)律:
(1)關(guān)于x軸對(duì)稱的點(diǎn),橫坐標(biāo)相同,縱坐標(biāo)、豎坐標(biāo)互為相反數(shù);
(2)關(guān)于y軸對(duì)稱的點(diǎn),縱坐標(biāo)相同,橫坐標(biāo)、豎坐標(biāo)互為相反數(shù);
(3)關(guān)于原點(diǎn)對(duì)稱的點(diǎn),橫坐標(biāo)、縱坐標(biāo)、豎坐標(biāo)都互為相反數(shù).