2023 AMC 8 第 7 题

先试着解答 2023 AMC 8 第 7 题,然后核对你的答案与视频与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2023 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

7.

一个边平行于 xx 轴和 yy 轴的矩形,其一对相对顶点为 (15,3)(15, 3) 和 (16,5)(16, 5)。一条直线经过点 A(0,0)A(0, 0) 和 B(3,1)B(3, 1)。另一条直线经过点 C(0,10)C(0, 10) 和 D(2,9)D(2, 9)。矩形上有多少个点至少在这两条直线之一上?
A rectangle, with sides parallel to the xx-axis and yy-axis, has opposite vertices located at (15,3)(15, 3) and (16,5).(16, 5). A line is drawn through points A(0,0)A(0, 0) and B(3,1).B(3, 1). Another line is drawn through points C(0,10)C(0, 10) and D(2,9).D(2, 9). How many points on the rectangle lie on at least one of the two lines?
00
11
22
33
44
答案:B
知识点:坐标几何一次方程
小提示:
写出两条直线的方程
Find the equations of the two lines
大提示:
矩形满足 15≤x≤1615\le x\le16 且 3≤y≤53\le y\le5
The rectangle has 15≤x≤1615\le x\le16 and 3≤y≤53\le y\le5
视频讲解:
解答视频缩略图
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文字解答:
画出这两条直线。
从图中可见,只有矩形左上角落在其中一条直线上。
所以正确答案是 B。
We can graph the two lines.
From this, we see that only the top left corner of the rectangle intersects either line.
Thus, B is the correct answer.
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