AMC8 2005

AMC8 2005 · Q7

AMC8 2005 · Q7. It mainly tests Fractions, Pythagorean theorem.

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

比尔向南走 1/2 英里，然后向东走 3/4 英里，最后向南走 1/2 英里。他与起点直线距离有多少英里？

(A) 1 1

(B) 1 1/4 1 1/4

(D) 1 3/4 1 3/4

(E) 2 2

Answer

Correct choice: (B)

正确答案：（B）

Solution

(B) The diagram on the left shows the path of Bill’s walk. As the diagram on the right illustrates, he could also have walked from $A$ to $B$ by first walking 1 mile south then $\frac{3}{4}$ mile east. By the Pythagorean Theorem, $(AB)^2 = 1^2 + \left(\frac{3}{4}\right)^2 = 1 + \frac{9}{16} = \frac{25}{16},$ so $AB = \frac{5}{4} = 1\frac{1}{4}.$

（B）左边的图显示了比尔步行的路径。如右边的图所示，他也可以从 $A$ 到 $B$，先向南走 1 英里，再向东走 $\frac{3}{4}$ 英里。根据勾股定理， $(AB)^2 = 1^2 + \left(\frac{3}{4}\right)^2 = 1 + \frac{9}{16} = \frac{25}{16},$ 所以 $AB = \frac{5}{4} = 1\frac{1}{4}$。

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