Question

18．如圖，數(shù)軸上點(diǎn)A，B所對(duì)應(yīng)的實(shí)數(shù)分別是1和$\sqrt{2}$，點(diǎn)B與點(diǎn)C關(guān)于點(diǎn)A對(duì)稱(chēng)，則點(diǎn)C所對(duì)應(yīng)的實(shí)數(shù)是（　�。�

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

Answer 1

分析 根據(jù)點(diǎn)A、B表示的數(shù)求出AB，再根據(jù)對(duì)稱(chēng)可得AC=AB，然后根據(jù)數(shù)軸上左邊的數(shù)比右邊的小列式計(jì)算即可得解．

解答 解：∵點(diǎn)A，B所對(duì)應(yīng)的實(shí)數(shù)分別是1和$\sqrt{2}$，
∴AB=$\sqrt{2}$-1，
∵點(diǎn)B與點(diǎn)C關(guān)于點(diǎn)A對(duì)稱(chēng)，
∴AC=AB，
∴點(diǎn)C所對(duì)應(yīng)的實(shí)數(shù)是1-（$\sqrt{2}$-1）=1-$\sqrt{2}$+1=2-$\sqrt{2}$．
故選B．

點(diǎn)評(píng) 本題考查了實(shí)數(shù)與數(shù)軸，點(diǎn)的對(duì)稱(chēng)，解題關(guān)鍵是求數(shù)軸上兩點(diǎn)間的距離應(yīng)讓較大的數(shù)減去較小的數(shù)即可．