AMC 8 2019 Problem 6

AMC8 2019 年第 6 题

概率★★☆☆☆

There are 81 grid points (uniformly spaced) in the square shown in the diagram below, including the points on the edges. Point P is in the center of the square. Given that point Q is randomly chosen among the other 80 points, what is the probability that the line PQ is a line of symmetry for the square?

在下图所示的正方形中，一共有 81 个格点（均匀分布），包括边上的点。点 P 位于正方形的中心。已知点 Q 是从其他 80 个点中随机选择的一个点，问直线 PQ 是正方形的一条对称轴的概率是多少？

A. $\displaystyle \frac{1}{5}$
B. $\displaystyle \frac{1}{4}$
C. $\displaystyle \frac{2}{5}$
D. $\displaystyle \frac{9}{20}$
E. $\displaystyle \frac{1}{2}$

正确答案 · Correct Answer

解析 · Solution

Solution 1

Lines of symmetry go through point

P

, and there are 8 directions the lines could go, and there are 4 dots at each direction.

\displaystyle \frac{4×8}{80} = \frac{2}{5}

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