Question

Crystal 为每日跑步规划了一条路线。她先向正北跑一英里，然后向东北跑一英里，再向东南跑一英里。最后一段她沿直线跑回起点。最后一段长多少英里？

Crystal has a running course marked out for her daily run. She starts this run by heading due north for one mile. She then runs northeast for one mile, then southeast for one mile. The last portion of her run takes her on a straight line back to where she started. How far, in miles, is this last portion of her run?

$1$

$\sqrt{2}$

$\sqrt{3}$

$2$

$2\sqrt{2}$

答案：C

知识点：勾股定理向量

难度评级：1220

解答：

从图中可以看出，最后一段是一个直角三角形的斜边。

一条直角边来自正北方向的 $1$ 英里，另一条直角边为 $\sqrt{1^2 + 1^2} = \sqrt2.$

因此最后一段距离为 $\sqrt{\sqrt2^2 + 1^2} = \sqrt3.$

所以正确答案是 C。

From the diagram, we see that the distance traveled is the hypotenuse of a right triangle.

One of the legs is just $1$ from running due north. The other leg is $\sqrt{1^2 + 1^2} = \sqrt2.$

The final distance is then $\sqrt{\sqrt2^2 + 1^2} = \sqrt3.$

Thus, C is the correct answer.

2010 AMC 10A 第 7 题

答案：C

难度评级：1220

解答：

其他年份的第 7 题