名校
1 . 在直角坐标平面
上的一列点
,简记为
.若由
构成的数列
满足
,其中
为方向与
轴正方向相同的单位向量,则称
为
点列.
(1)判断
,是否为
点列,并说明理由;
(2)若
为
点列,且点
在点
的右上方.任取其中连续三点
,判断
的形状(锐角三角形、直角三角形、钝角三角形),并予以证明;
(3)若
为
点列,正整数
,满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c13b920ec4a33103954c68daa7644ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7836415e9b77334eee27c0d497ca5ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b7daef66f5d193befe316e6a9df2bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821a7c2e810ef18a2ee78f3722f03c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b7813755384e0b6044fe296d7c6029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a09e3d201f7699e8d480c768e34696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6edc135bb869e8e8dd68b711d147e368.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06dfbe171fd6d47d6b8ab101b62ac0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ada35c9021498f44a4c7cb9efd058bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e71cb7bfc09205b70196aeadad57439.png)
您最近一年使用:0次
2020-06-26更新
|
577次组卷
|
7卷引用:上海市黄浦区格致中学2015-2016学年高二上学期第二次测验数学试题
2 . 我们知道,在平面内,有公共原点且互相垂直的两条数轴构成平面直角坐标系,同样地,在平面内有公共原点且不垂直的两条数轴构成的坐标系,我们称之为“斜坐标系”.如图,在斜坐标系中,两条坐标轴的公共原点称为斜坐标系的原点,其坐标记为
,点
是斜坐标系
中的任意一点,与直角坐标系相类似,过点
分别作两坐标轴的平行线,与
轴、
轴交于点
、
,若
、
在
轴、
轴上分别对应实数
、
,则有序数对
叫做点
在斜坐标系
中的坐标,记为
.若点
、
是斜坐标系
(
)中任意两点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/02ac5da5-9e1c-4f9a-bd76-6f2d1756a2f7.png?resizew=152)
(1)求点
、
之间的距离
(用坐标表示);
(2)若点
分有向线段
成定比
,请你推导点
坐标在斜坐标系中的定比分点公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b6a9ffffc0c461881b427c543924cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827539d066d1b78e7ef8bc1569864971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a53e311ee0b5085e7e5a45c606daa5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad4c21d0009cf8265361890308e056e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/02ac5da5-9e1c-4f9a-bd76-6f2d1756a2f7.png?resizew=152)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec28989d516a0d990a517232788cbec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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