2. 外语
  3. In the xy-plane, a quadrilateral has vertices at(-1, 4),(7,4),(7, -5), and(-1, -5). What is the perimeter of the quadrilateral?

In the xy-plane, a quadrilateral has vertices at(-1, 4),(7,4),(7, -5), and(-1, -5). What is the perimeter of the quadrilateral?

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问题 In the xy-plane, a quadrilateral has vertices at(-1, 4),(7,4),(7, -5), and(-1, -5). What is the perimeter of the quadrilateral?
选项 A、17
B、18
C、19
D、32
E、34
答案E
解析 A sketch of the quadrilateral with vertices at(-1,4),(7,4),(7, -5), and(-1, -5)is shown in the xy-plane below.

From the figure you can see that two of the sides of the quadrilateral are horizontal and two are vertical. Therefore the quadrilateral is a rectangle. Since the points(-1, -5)and(7, -5)are endpoints of one of the horizontal sides, the length of each horizontal side is 7 -(-1), or 8. Since the points(-1,4)and(-1,-5)are endpoints of one of the vertical sides, the length of each vertical side is 4 -(-5), or 9. Therefore the perimeter of the rectangle is 2(8 + 9), or 34. The correct answer is Choice E.
This explanation uses the following strategies.
Strategy 2: Translate from Words to a Figure or Diagram
Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation
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