AMC8 2003

AMC8 2003 · Q24

AMC8 2003 · Q24. It mainly tests Circle theorems, Coordinate geometry.

A ship travels from point A to point B along a semicircular path, centered at Island X. Then it travels along a straight path from B to C. Which of these graphs best shows the ship’s distance from Island X as it moves along its course?

一艘船从点A到点B沿以岛X为圆心的半圆路径行驶。然后从B到C沿直线路径行驶。以下哪个图像最好显示了船沿航线移动时与岛X的距离？

(A)

(B)

(C)

(D)

(E)

Answer

Correct choice: (B)

正确答案：（B）

Solution

(B) All points along the semicircular part of the course are the same distance from X, so the first part of the graph is a horizontal line. As the ship moves from B to D, its distance from X decreases, then it increases as the ship moves from D to C. Only graph B has these features.

（B）航线的半圆部分上所有点到 \(X\) 的距离都相同，因此图像的第一部分是一条水平线。当船从 \(B\) 移动到 \(D\) 时，它到 \(X\) 的距离减小；随后当船从 \(D\) 移动到 \(C\) 时，这个距离又增大。只有图像 \(B\) 具有这些特征。

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