1954 AMC 12 第 45 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。
45.
在菱形 内作若干平行于对角线 的线段，线段端点位于菱形的边上。以线段到顶点 的距离为自变量、线段长度为函数值作图。该图像为：
In a rhombus line segments are drawn within the rhombus, parallel to diagonal and terminated in the sides of the rhombus. A graph is drawn showing the length of a segment as a function of its distance from vertex The graph is:
一条经过原点的直线。
a straight line passing through the origin.
一条穿过第一象限的直线。
a straight line cutting across the upper right quadrant.
两条组成正立 形的线段
two line segments forming an upright
两条组成倒置 形的线段
two line segments forming an inverted
以上答案均不正确。
none of these.
小提示：
想象把一条平行于 的线段从 向对面顶点移动
Imagine moving a segment parallel to from toward the opposite vertex
大提示：
线段长度先线性增加到整条对角线的长度，再线性减小到零
Its length grows linearly to the full diagonal and then decreases linearly to zero
解答：
从 出发时，平行截线的长度为 ，然后线性增加，直至达到对角线 的长度。继续向对面顶点移动时，线段长度线性减小回 。因此图像由两条组成倒 形的线段构成。
因此，正确答案是 D。
Starting at the parallel cross section has length and grows linearly until it reaches the diagonal Continuing toward the opposite vertex, its length decreases linearly back to The graph is therefore made of two line segments forming an inverted
Thus, the correct answer is D.