1970 AMC 12 第 26 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
26.
在 平面内，考虑图形 和图形 这两个图形有多少个不同的公共点？
The number of distinct points in the -plane common to the graphs of and is:
无穷多个
infinite
小提示：
每个乘积方程都表示两条直线的并集
Each product equation represents a union of two lines
大提示：
先检查每组两条直线的交点，再考虑四种配对
Check the intersection of the two lines in each pair before considering all four pairings
解答：
第一个图形是以下两条直线的并集：这两条直线交于 。第二个图形是以下两条直线的并集：它们也交于 。事实上，将 代入可知，它满足四条直线的方程。由于四条直线的斜率各不相同，不会有其他点同时属于两个图形。因此恰有一个公共点。
因此，正确答案是 B。
The first graph is the union of and those two lines meet at The second graph is the union of and these also meet at In fact, substituting satisfies all four line equations. Since the four lines have distinct slopes, no other point can belong to a line from each graph. There is exactly one common point.
Therefore, the correct answer is B.
其他年份的第 26 题
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- 1999 AMC 12