Question

17．在如圖所示的數(shù)軸上，點(diǎn)B與點(diǎn)C關(guān)于點(diǎn)A對(duì)稱，A，B兩點(diǎn)對(duì)應(yīng)的實(shí)數(shù)分別是$\sqrt{2}$和-1，則點(diǎn)C所對(duì)應(yīng)的實(shí)數(shù)是（　�。�

• A． 1+$\sqrt{2}$
• B． 2+$\sqrt{2}$
• C． 2$\sqrt{2}$-1
• D． 2$\sqrt{2}$+1

Answer 1

分析 根據(jù)兩點(diǎn)關(guān)于中點(diǎn)對(duì)稱，可得線段的中點(diǎn)，根據(jù)線段中點(diǎn)的性質(zhì)，可得答案．

解答 解：設(shè)C點(diǎn)坐標(biāo)為x，
由點(diǎn)B與點(diǎn)C關(guān)于點(diǎn)A對(duì)稱，得
AC=AB，即x-$\sqrt{2}$=$\sqrt{2}$+1，
解得x=2$\sqrt{2}$+1．
故選：D．

點(diǎn)評(píng) 本題考查了實(shí)數(shù)與數(shù)軸，利用兩點(diǎn)關(guān)于中點(diǎn)對(duì)稱得出線段的中點(diǎn)是解題關(guān)鍵．