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 
?
The Correct answer is B.
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.
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.
