2013年6月9日SAT考试官方每日一题

考试类型: Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

, , , and  are points on a line, with  the midpoint of segment . The lengths of segments , , and  are , , and , respectively. What is the length of segment ?

A.

B.

C.

D.

E.

正确答案:B

解析:

The key to this question lies in not jumping to incorrect conclusions. The question names the points on a line. It gives you a variety of information about the points. The one thing it does not do is tell you the order in which the points fall.

Many students assume that the order of the points is , then ,  then ,  then .As you will see, if you try to locate the points in this order, you will be unable to answer the question.

What Is the Question Asking?

The question asks for the length of line segment . In order to find this length, you have to establish the relative positions of the four points on the line.

What Do You Know?

Try to draw the figure. You might be tempted to locate point  first. Unfortunately, you don't have enough information about , yet, to place it.

You can place ,, and  because  is the midpoint of .

You know the lengths of three of the line segments:

Because you know where  is, you can label the length of .

Build the Figure, Adding What You Know and What You Can Figure Out

Because  is the midpoint of , you know that  and  are each  units long.

Where can you place point ?

It has to be  units from , because .
It also has to be  units from , because .
So the only location for  is between  and , but closer to .

Place point  and mark the distances.

It is now an easy matter to figure out the answer to the question:

 is  units.
 is  units closer to  than , so  is  units.

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