A line segment is a piece, or part, of a line. The line segment is represented by endpoints on each end of the line segment. A line in geometry is represented by a line with arrows at each end which goes on forever. A line segment and a line are different because a line goes on forever while a line segment has a distinct beginning and end and it is measurable. In other words, A line segment is a track between two points that can be measured. Since line segments have a defined length, they can form sides of any polygon.

LINE SEGMENT-

A line segment is represented by a bar on top of the edge name which is the line segment symbol. It is written as      ¯¯¯A  ¯¯B¯¯

HOW TO MEASURE LINE SEGMENTS?

Line segments can be measured with the help of a scale or ruler. Let us see how to measure a given line segment PQ.

• Step 1: Place the tip of the ruler/scale carefully so that zero is placed at the starting point P of the line segment.
• Step 2: Now, start reading the values in the ruler on the ruler and spot the number which comes on the other endpoint of the line Q.
• Step 3: Thus, the length of the line segment PQ is 4 inches, which can be written as ¯¯¯¯P¯¯Q¯¯¯ = 4 inches.

LINE SEGMENT FORMULA-

In the above example, we measured the length of line segment PQ which was 4 inches. Now, let us see how to find the length of a line segment when the coordinates of the two endpoints are given from a graph. In this case, we will use the distance formula, that is, D = √[(x₂−x₁)² + (y₂−y₁)²] . Here, (x₁, y₁) and (x₂, y₂) are the coordinates of the given points.

For example, let us consider the line segment has the following coordinates: (-2, 1) and (4, –3). Now Let us apply the distance formula to find the length of the line segment formed by those points. Here, x₁ = -2; x₂ = 4; y₁ = 1; y₂ = -3 After substituting the values in the distance formula we get: D =√[(4-(-2))² + (-3-1)²) = √((4+2)2² + (-3-1)²] = √(62 + (-4)²) = √(36 + 16) = √52 = 7.21 units. Thus, using the distance formula, we found that the length of the line segment with the given coordinates (-2, 1) and (4, –3) is 7.21 units.

Difference Between Line, Line Segment, and Ray

In order to understand the difference between a line, a line segment, and a ray, below is the description of the line, line segment, and ray.

LINE–

• Line is defined as the set of points that can be extended in two opposite directions.
• It is represented with arrows at both ends to tell us that it can be extended indefinitely.

LINE SEGMENT-

• A line segment is a part of a line that has a beginning as well as an endpoint.
• It is represented with two endpoints and has a definite length.

RAY–

• A  ray is a part of a line. Ray has a starting point but no endpoint.
• It can be denoted by one start point and on the other end an arrow which means that it goes on forever through one direction.

FEW FACTS ABOUT THE LINE SEGMENT-

• A line has no ends and cannot be measured.
• A line segment has a start point and an endpoint, therefore, it can be measured.
• Line segments have a defined length, thus, they can form the sides of any polygon.
• A ray has just one start point but no endpoint, therefore, it cannot be measured.
• The concept of rays can be understood with the example of the rays of the sun, which have a beginning point but no endpoint.

CONCLUSION-

A line segment is a piece, or part, of a line. The line segment is represented by endpoints on each end of the line segment. A line in geometry is represented by a line with arrows at each end which goes on forever. A line segment and a line are different because a line goes on forever while a line segment has a distinct beginning and end and it is measurable. In other words, A line segment is a track between two points that can be measured. Since line segments have a defined length, they can form sides of any polygon.

• A line has no ends and cannot be measured.
• A line segment has a start point and an endpoint, therefore, it can be measured.
• Line segments have a defined length, thus, they can form the sides of any polygon.
• A ray has just one start point but no endpoint, therefore, it cannot be measured.
• The concept of rays can be understood with the example of the rays of the sun, which have a beginning point but no endpoint.