AMC10 2007 B
AMC10 2007 B · Q10
AMC10 2007 B · Q10. It mainly tests Area & perimeter, Ratios in geometry.
Two points B and C are in a plane. Let S be the set of all points A in the plane for which $\triangle ABC$ has area 1. Which of the following describes S?
平面上有两点B和C。让S为平面中所有点A的集合，使得$\triangle ABC$的面积为1。以下哪项描述了S？
(A)
two parallel lines
两条平行线
(B)
a parabola
一条抛物线
(C)
a circle
一个圆
(D)
a line segment
一条线段
(E)
two points
两点
Answer
Correct choice: (A)
正确答案：（A）
Solution
Answer (A): If the altitude from $A$ has length $d$, then $\triangle ABC$ has area $(1/2)(BC)d$. The area is $1$ if and only if $d = 2/(BC)$. Thus $S$ consists of the two lines that are parallel to line $BC$ and are $2/(BC)$ units from it, as shown.
答案（A）：如果从$A$作高的长度为$d$，那么$\triangle ABC$的面积为$(1/2)(BC)d$。当且仅当$d = 2/(BC)$时，面积为$1$。因此，$S$由两条与直线$BC$平行且与其距离为$2/(BC)$个单位的直线组成，如图所示。
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