1 . 在平面直角坐标系
中,对于任意一点
,总存在一个点
满足关系式:
(
,
),则称
为平面直角坐标系中的伸缩变换.
(1)在同一直角坐标系中,求平面直角坐标系中的伸缩变换
,使得椭圆
变换为一个单位圆;
(2)在同一直角坐标系中,△
(
为坐标原点)经平面直角坐标系中的伸缩变换
(
,
)得到△
,记△
和△
的面积分别为S与
,求证:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2beb91f10d2d8f2aa0dcc3f5cd1598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fb4db5074e7c8945c1800f1cc324be9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754780ccfb7aea6a9902a11e490c94cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f8964e0587e20d06a9a401808cb4575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf73db6da96b2e3ef7b70beecb22363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00efb6b051a61e5a1f0a6b429b616974.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
(1)在同一直角坐标系中,求平面直角坐标系中的伸缩变换
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795b28d4816617d5f344dce62d7a533.png)
(2)在同一直角坐标系中,△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571f8dfb1eb003438f27bab2324140ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/425b7513e7aaa5306945435e48604bff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf73db6da96b2e3ef7b70beecb22363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00efb6b051a61e5a1f0a6b429b616974.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb48c5f1c6e24fe7b8944ad007795e02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571f8dfb1eb003438f27bab2324140ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb48c5f1c6e24fe7b8944ad007795e02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e030dbd6f1af3802272609cca6f1148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1c7abe77a98f5df66d9bd3111e9dfb.png)
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