2019 AMC 12A 第 6 题
先试着解答 2019 AMC 12A 第 6 题，然后核对你的答案与精心整理的解答，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 2019 AMC 12A 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。
6.
下图显示了直线 以及由正方形和线段组成的一个规则、无限、重复的图案。
在绘制此图形的平面中，下面四类刚体运动变换中，除恒等变换外，有多少类中的某个变换会把这个图形变到自身？
• 绕直线 上某点的某个旋转
• 沿平行于直线 方向的某个平移
• 关于直线 的反射
• 关于某条垂直于直线 的直线的某个反射
The figure below shows line with a regular, infinite, recurring pattern of squares and line segments.
How many of the following four kinds of rigid motion transformations of the plane in which this figure is drawn, other than the identity transformation, will transform this figure into itself?
• some rotation around a point of line
• some translation in the direction parallel to line
• the reflection across line
• some reflection across a line perpendicular to line
小提示：
平移一个完整周期显然可行
A translation by one period clearly works
大提示：
测试绕 上某点旋转 ，并检查两个反射是否能正确映射对角线段
Test a rotation about a point on and check that neither reflection maps the diagonal segments correctly
解答：
平移一个完整周期会把图形映到自身，所以平移可行。
绕 上适当的点旋转 会把直线上方的每个正方形送到直线下方的正方形，并且对角线段也对应，因此这个旋转可行。
关于 的反射会把上方朝右上的对角线送到下方朝右上的对角线，但实际下方的对角线朝左下，因此失败。关于垂直直线的反射也因同样原因失败。四类变换中只有 类可行。
所以正确答案是 C。
A translation by one full period maps the figure to itself, so translation works.
A rotation about a suitable point on sends each square above the line to the square below it, with the diagonal segments matching, so this rotation works.
Reflection across sends the top-right diagonals to top-right diagonals below the line, but the actual below-line diagonals point to the bottom-left, so it fails. A reflection across a perpendicular line fails for the same reason. Only of the four transformations work.
Thus, the correct answer is C.
其他年份的第 6 题
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