# Question of the Day

## Can you answer today's question?

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Dec
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Mathematics > Standard Multiple Choice

, , , 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 ?

# Right-o!

### Explanation

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.

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.