2. 外语
  3. Points A, B, C, and D are on the number line above, and AB = CD =(BC). What is the coordinate of C ?

Points A, B, C, and D are on the number line above, and AB = CD =(BC). What is the coordinate of C ?

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问题
Points A, B, C, and D are on the number line above, and AB = CD =(BC). What is the coordinate of C ?
选项 A、 
B、 
C、 
D、 
E、 
答案D
解析 From the figure you can see that since the coordinate of A is 1/3, it follows that the coordinate of C is 1/3+AB+BC. Since you are given that AB =(BC), the coordinate of C can be rewritten in terms of AB as follows:
+AB+BC =+AB+3(AB)=+ 4(AB)
To find the coordinate of C, you need to know AB. From the figure, you know that AD = AB+BC+CD = AB+3(AB)+AB = 5(AB). On the other hand, since the coordinate of A is 1/3 and the coordinate of D is 1/2, it follows that AD == 1/6.
Therefore you can conclude that 1/6 = 5(AB)and AB = 1/30. Thus the coordinate of C is, or 7/15. The correct answer is Choice D.
This explanation uses the following strategies.
Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation
Strategy 8: Search for a Mathematical Relationship
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