一束光線從點(diǎn)A(3,3)出發(fā),經(jīng)過y軸上點(diǎn)C反射后經(jīng)過點(diǎn)B(1,0),則光線從A點(diǎn)到B點(diǎn)經(jīng)過的路線長是( ?。?br/>A. 4
B. 5
C. 6
D. 7
如果將y軸當(dāng)成平面鏡,設(shè)A點(diǎn)關(guān)于y軸的對(duì)稱點(diǎn)為A′,則由光路知識(shí)可知,A′相當(dāng)于A的像點(diǎn),光線從A到C到B,相當(dāng)于光線從A′直接到B,所以C點(diǎn)就是A′B與y軸的交點(diǎn).
∵A點(diǎn)關(guān)于y軸的對(duì)稱點(diǎn)為A′,A(3,3),
![](http://hiphotos.baidu.com/zhidao/pic/item/83025aafa40f4bfbc7c218e2004f78f0f7361871.jpg)
∴A′(-3,3),
進(jìn)而由兩點(diǎn)式寫出A′B的直線方程為:y=
?(x-1).
令x=0,求得y=
.所以C點(diǎn)坐標(biāo)為(0,
).
那么根據(jù)勾股定理,可得:
AC=
=
,BC=
=
.
因此,AC+BC=5.
故選B.