AMC8 2023
AMC8 2023 · Q7
AMC8 2023 · Q7. It mainly tests Coordinate geometry, Transformations.
A rectangle, with sides parallel to the $x$-axis and $y$-axis, has opposite vertices located at $(15, 3)$ and $(16, 5)$. A line is drawn through points $A(0, 0)$ and $B(3, 1)$. Another line is drawn through points $C(0, 10)$ and $D(2, 9)$. How many points on the rectangle lie on at least one of the two lines?
一个矩形，其边平行于 $x$ 轴和 $y$ 轴，对角顶点位于 $(15, 3)$ 和 $(16, 5)$。一条直线通过点 $A(0, 0)$ 和 $B(3, 1)$。另一条直线通过点 $C(0, 10)$ 和 $D(2, 9)$。矩形上有多少点位于至少一条直线上？
(A)
\ 0
\ 0
(B)
\ 1
\ 1
(C)
\ 2
\ 2
(D)
\ 3
\ 3
(E)
\ 4
\ 4
Answer
Correct choice: (B)
正确答案：（B）
Solution
If we extend the lines, we have the following diagram:
Therefore, we see that the answer is $\boxed{\textbf{(B)}\ 1}.$
如果我们延伸这些直线，我们有以下图示：
因此，我们看到答案是 $\boxed{\textbf{(B)}\ 1}$。
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