Question

$xy$ 平面中坐标为 $(1000, 2012)$ 的点关于直线 $y=2000$ 对称。对称点的坐标是什么？

The point in the $xy$ -plane with coordinates $(1000, 2012)$ is reflected across the line $y=2000.$ What are the coordinates of the reflected point?

$(998,2012)$

$(1000,1988)$

$(1000,2024)$

$(1000,4012)$

$(1012,2012)$

答案：B

知识点：反射（几何）坐标几何

难度评级：560

解答：

关于水平直线反射时，x 坐标不变。

点 $(1000,2012)$ 在 $y=2000$ 上方 $12$ 个单位，所以对称点在直线另一侧同样相距 $12$ 个单位，即 $(1000,1988)$ 。

所以正确答案是 B。

Notice that the line in question is perfectly horizontal. This means that if we were to construct a perpendicular line segment from the point to the line, to find the reflected coordinates of the point, we simply double the distance along that line segment.

The line segment from $(1000,2012)$ to $y=2000$ is of length $12,$ so the reflected point is along this same line segment, but a distance of $12$ on the other side of the horizontal line. This yields $(1000,1988).$

Thus, the correct answer is B .

2012 AMC 10B 第 3 题

答案：B

难度评级：560

解答：

其他年份的第 3 题