Question

Bill 先向南走 $\frac{1}{2}$ 英里，再向东走 $\frac{3}{4}$ 英里，最后又向南走 $\frac{1}{2}$ 英里。沿直线计算，他离起点有多少英里？

Bill walks $\frac{1}{2}$ mile south, then $\frac{3}{4}$ mile east, and finally $\frac{1}{2}$ mile south. How many miles is he, in a direct line, from his starting point?

$1$

$1 \frac{1}{4}$

$1 \frac{1}{2}$

$1 \frac{3}{4}$

$2$

答案：B

知识点：勾股定理分数

难度评级：940

解答：

所求是对角线长度。使用勾股定理： $\sqrt{\left(\dfrac{1}{2} + \dfrac{1}{2}\right)^2 + \dfrac{3}{4}^2}$ $= \sqrt{1 + \dfrac{9}{16}} = \sqrt{\dfrac{25}{16}} = \dfrac{5}{4}$

所以正确答案是 B。

Note that what we want is the length of the diagonal. We can use the Pythagorean theorem to find this. $\sqrt{\left(\dfrac{1}{2} + \dfrac{1}{2}\right)^2 + \dfrac{3}{4}^2}$ $= \sqrt{1 + \dfrac{9}{16}} = \sqrt{\dfrac{25}{16}} = \dfrac{5}{4}$

Thus, B is the correct answer.

2005 AMC 8 第 7 题

答案：B

难度评级：940

解答：

其他年份的第 7 题