Introduction

A line segment is part of a line that's bounded by two points, called the endpoints of the segment. A line segment with endpoints A and B, like the one shown below, is denoted by \overline{AB}.



The measure of a line segment is its length. For a line segment \overline{AB}, the measure is denoted by AB (with no line on top) to distinguish it from the line segment itself.

Watch out! The line segment \overline{AB} and its measure AB are not the same thing. The line segment \overline{AB} is a geometric object, while its measure AB (with no line on top) is a number. It's similar to how a person is a physical entity, while their height is a number.

Note: We could also express the segment as \overline{BA}, switching the order of the endpoints. The notations \overline{BA} and \overline{AB} represent the same exact segment. We could also write the length of the segment as BA or AB.

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Example: Understanding Line Segment Notation

Suppose that a line segment has a length of 2\,\textrm{m}, and that A and B are its endpoints. Which of the following statements are true?

  1. \overline{AB} = 2\,\textrm{m}
  2. \overline{BA} = 2\,\textrm{m}
  3. AB = 2\,\textrm{m}
EXPLANATION

Let's check each statement in turn.

  • Statement I is false. The notation \overline{AB} represents the line segment itself, not the length of the line segment. Therefore, the expression {\overline{AB}}=2\,\textrm{m} is not valid. Instead, it should say AB = 2 \, \textrm{m}.

  • Statement II is false. Since \overline{BA} represents the line segment itself, not the length of the line segment. Therefore, the expression {\overline{BA}}=2\,\textrm{m} is not valid.

  • Statement III is true. The notation AB represents the length of the line segment \overline{AB}, and this line segments has a length of 2\,\textrm{m}. Therefore, AB = 2\,\textrm{m} is a correct statement.

Therefore, the correct answer is "III only".

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Practice: Understanding Line Segment Notation

Suppose that a line segment has a length of $4$ units, and that $P$ and $Q$ are its endpoints. Which of the following statements are true?

  1. $\overline{PQ} = 4$
  2. $\overline{QP} = 4$
  3. $\dfrac{PQ}{2} = 1$
a
 None
b
 I and II only
c
 II only
d
 II and III only
e
 I and III only
Practice: Understanding Line Segment Notation

Suppose that a line segment has a length of $6\,\textrm{cm},$ and that $A$ and $B$ are its endpoints. Which of the following statements are true?

  1. $\overline{AB} = 6\,\textrm{cm}$
  2. $\overline{BA} = 6\,\textrm{cm}$
  3. $AB = 6\,\textrm{cm}$
a
 III only
b
 I and III only
c
 II only
d
 None
e
 I and II only
Example: Calculating the Measure of a Line Segment on a Grid

What is the measure of the line segment \overline{ML} shown below?



EXPLANATION

Note that the length of a side of one cell is \dfrac{10\,\textrm{mm}}{2} = 5\,\textrm{mm}.

The line segment has a length of 7 cells, so the total measure is ML = 7 \cdot 5\,\textrm{mm} = 35\,\textrm{mm}.

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Practice: Calculating the Measure of a Line Segment on a Grid

What is the measure of the line segment $\overline{PQ}$ shown above?

a
 $2\,\textrm{mi}$
b
 $4\,\textrm{mi}$
c
 $1\,\textrm{mi}$
d
 $5\,\textrm{mi}$
e
 $3\,\textrm{mi}$
Practice: Calculating the Measure of a Line Segment on a Grid

What is the measure of the line segment $\overline{PQ}$ shown above?

a
 $8\,\textrm{mm}$
b
 $5\,\textrm{mm}$
c
 $6\,\textrm{mm}$
d
 $3\,\textrm{mm}$
e
 $4\,\textrm{mm}$
Measuring a Line Segment

To measure a line segment, we use a ruler as follows:

  1. Align the ruler along the line segment in such a way that one of the endpoints corresponds to the zero-mark on the ruler.


  2. Read the measurements that correspond to the second endpoint of the segment.


Given that this particular ruler measures length in centimeters ( \textrm{cm} ), we conclude that AB = 5\,\textrm{cm}.

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Example: Calculating the Measure of a Line Segment Using a Ruler

The ruler shown below allows measuring length both in \textrm{cm} (centimeters) and \textrm{in} (inches). Determine the measure of the line segment \overline{MN}.



EXPLANATION

Note that M is not aligned with the zero-mark on the ruler.

To find the length, we read the values that correspond to the points M and N, and take the difference.

From the picture, we see that M corresponds to 0.5\,\textrm{in} while N corresponds to 2\,\textrm{in}.

Therefore, \begin{align*} MN = 2\,\textrm{in}-0.5\,\textrm{in}=1.5\,\textrm{in}. \end{align*}

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Practice: Calculating the Measure of a Line Segment Using a Ruler

Determine the measure of the segment $\overline{AB}$ shown above.

a
 $2.5\,\textrm{in}$
b
 $2\,\textrm{in}$
c
 $0.5\,\textrm{in}$
d
 $1\,\textrm{in}$
e
 $1.5\,\textrm{in}$
Practice: Calculating the Measure of a Line Segment Using a Ruler

Which segments have a length of $2\,\textrm{in}?$

a
 $\overline{RS}$ only
b
 $\overline{PQ}$ only
c
 $\overline{PQ}$ and $\overline{TV}$ only
d
 $\overline{PQ}$ and $\overline{RS}$ only
e
 $\overline{TV}$ only
Example: Calculating the Measure of a Line Segment on a Number Line

Find the length of the line segment \overline{AB} shown below.



EXPLANATION

To find the length, we read the values that correspond to the points A and B and take the difference.

From the diagram, we see that A corresponds to 10 units while B corresponds to 50 units.

Therefore, we conclude that AB = 50 - 10 = 40\,\textrm{units}.

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Practice: Calculating the Measure of a Line Segment on a Number Line

Find the length of the line segment $\overline{AB}$ shown above.

a
 $8$
b
 $7$
c
 $6$
d
 $4$
e
 $10$
Practice: Calculating the Measure of a Line Segment on a Number Line

Find the length of the line segment $\overline{AB}$ shown above.

a
 $10$
b
 $7$
c
 $8$
d
 $9$
e
 $6$
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