Question

最少还必须涂黑多少个小正方形，才能使对角线 $\overline{BD}$ 成为正方形 $ABCD$ 的一条对称轴？

What is the minimum number of small squares that must be shaded so that a line of symmetry lies on the diagonal $\overline{BD}$ of square $ABCD$ ?

$1$

$2$

$3$

$4$

$5$

答案：D

知识点：对称性变换

难度评级：660

解答：

要使对角线 $\overline{BD}$ 成为对称轴，对角线外每个已涂黑小正方形都必须在对角线另一侧有一个对应的反射涂黑小正方形。

有 $4$ 个已涂黑小正方形的反射位置尚未涂黑，所以还必须涂黑 $4$ 个小正方形。

所以正确答案是 D。

For diagonal $\overline{BD}$ to be a line of symmetry, every shaded square off the diagonal must have a matching reflected shaded square on the other side of the diagonal.

There are $4$ shaded squares whose reflected partners are not shaded, so $4$ additional small squares must be shaded.

Thus, D is the correct answer.

2005 AMC 8 第 3 题

答案：D

难度评级：660

解答：

其他年份的第 3 题