tianlwsya
幼苗
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B。
如图,作点C关于x轴的对称点C
1 ,连接C
1 D交x轴于点M,连接CM。
则根据轴对称的性质和三角形三边关系,此时MC+MD的值最小。
∵点A(-1,0)在抛物线
![](https://img.yulucn.com/upload/4/81/48121d46f98dbfb9a2cab69b3acfb0bd_thumb.jpg)
,
∴
![](https://img.yulucn.com/upload/1/42/1422db10035451c9b8b2d3d2c032b69d_thumb.jpg)
,解得
![](https://img.yulucn.com/upload/b/9a/b9ae7ac0d3089807fdb02c105160f6a1_thumb.jpg)
。∴抛物线解析式为
![](https://img.yulucn.com/upload/2/1c/21c16228e7ab955103c69a7e1e28b10c_thumb.jpg)
。
又∵
![](https://img.yulucn.com/upload/2/1f/21f0b8bcea11d379c251a8f5b3683ea9_thumb.jpg)
,∴点D的坐标为
![](https://img.yulucn.com/upload/d/c7/dc794a8b83b9d941453e61f02bb490f7_thumb.jpg)
。
在
![](https://img.yulucn.com/upload/2/1c/21c16228e7ab955103c69a7e1e28b10c_thumb.jpg)
中,令x=0,得
![](https://img.yulucn.com/upload/d/ae/daed4108d83a1206624b7d63afe8e54b_thumb.jpg)
,∴点C的坐标为(0,-2),点C
1 的坐标为(0, 2)。
设直线C
1 D:
![](https://img.yulucn.com/upload/9/ae/9aee7baca29bf04aefb37d57ffffa01a_thumb.jpg)
,由C
1 (0, 2),D
![](https://img.yulucn.com/upload/d/c7/dc794a8b83b9d941453e61f02bb490f7_thumb.jpg)
得
![](https://img.yulucn.com/upload/b/f4/bf4463ec687d1d6f7c8d74fca7f83d20_thumb.jpg)
,解得
![](https://img.yulucn.com/upload/c/b5/cb540777014c222c72bec27dde685577_thumb.jpg)
。∴直线C
1 D:
![](https://img.yulucn.com/upload/5/a8/5a8ddb3e7d0c16e725e976faabff0866_thumb.jpg)
。
令y=0,即
![](https://img.yulucn.com/upload/f/94/f94bdaae93ae261204b5890392fe5ec8_thumb.jpg)
,解得
![](https://img.yulucn.com/upload/d/6a/d6a8d4876cb526b8f24aeb4581fdbebb_thumb.jpg)
。∴
![](https://img.yulucn.com/upload/4/bf/4bf09b4723f47f0890f760aa407e0d93_thumb.jpg)
。故选B。
1年前
4