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?

AMC 8 2003 Problem 24

AMC8 2003 年第 24 题

行程问题★★★☆☆

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

C

. Which of these graphs best shows the ship's distance from Island

X

as it moves along its course?

一艘船沿着以岛 X 为圆心的半圆形路径从点 A 航行到点 B。然后它沿着直线路径从 B 到 C。下面这些图表中哪一个最能显示当船沿航线行驶时，船与岛 X 的距离变化？

正确答案 · Correct Answer

Solution 1

The distance from Island

\text{X}

to any point on the semicircle will always be constant. On the graph, this will represent a straight line. The distance between Island

\text{X}

and line

\text{BC}

will not be constant though. We can easily prove that the distance between

\text{X}

and line

\text{BC}

will represent a curve. As the ship travels from

B

C

, the distance between the ship and Island

X

will first decrease until it reaches the point

Y

so that

\overline{XY}

is perpendicular to

\overline{BC}

, and then increase afterwards. Hence the answer choice that fits them all is

\text{(B)}

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