1 . 已知平面上四个点
,
,
,
.设
是四边形
及其内部的点构成的集合,点
是四边形对角线的交点,若集合
,则集合S所表示的平面区域的面积为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8232677e6eed1cd2e834665aa65e520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/791fe76f766e7b0d17f01c179fe2e394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c9c767265585104fe3cfa615b902c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5726a77e70012774fdc2eef269ad39b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289d7a880379d6060065c829b45b0ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92a292eaab7001822204c2a06a88d985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e367975cd9882f21334ffc8a92745161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5e3534b331b381343a72cce9f3e8e0d.png)
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解题方法
2 . 设直角坐标平面上两个区域为
,
,记
与
的公共部分面积为
.当
时,则
的表达式为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7b4d2af45f4af001a08d49d1161ee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c6d5db1f2427972e79de8f6eee18082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2709ca478fb15ea08e8aa55328eae8e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23865ee52040331dee23621b4a15c244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2709ca478fb15ea08e8aa55328eae8e6.png)
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3 . 已知O,A,B为平面上三点,若
,
,动点P和实数
,
满足
,
,
,则动点P轨迹的测度是__________ .(注:当动点的轨迹是曲线时,其测度指其长度;当动点的轨迹是平面区域时,其测度指该区域面积.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbabeab7e7d0e4bcd21a188362b5b9f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22905409f038387f0e954a47384b60a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59bca4c0ab83a3ca3b0ebf03281be74f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88b381aeca13cc17c8217a6db4d2c2ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a22570173ffa333a304977f3ee7df28.png)
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