What is a Line Segment?
A line segment is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon. The figure given below shows a line segment AB, where the length of line segment AB refers to the distance between its endpoints, A and B.
Line Segment Symbol
A line segment is represented by a bar on top which is the line segment symbol. It is written as
¯¯¯¯¯¯¯¯
AB
How to Measure Line Segments?
Line segments can be measured with the help of a ruler (scale). Let us see how to measure a given line segment and name it PQ.
Step 1: Place the tip of the ruler carefully so that zero is placed at the starting point P of the given line segment.
Step 2: Now, start reading the values given on the ruler and spot the number which comes on the other endpoint Q.
Step 3: Thus, the length of the line segment is 4 inches, which can be written as
¯¯¯¯¯¯¯¯
PQ= 4 inches.
Measuring a Line Segment
Line Segment Formula
In the above example, we measured the length of line segment PQ to be 4 inches. This is written as
¯¯¯¯¯¯¯¯
PQ
= 4 inches. Now, let us see how to find the length of a line segment when the coordinates of the two endpoints are given. In this case, we 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, a line segment has the following coordinates: (-2, 1) and (4, –3). Let us apply the distance formula to find the length of the line segment. Here, x1=-2; x2 = 4; y1= 1; y2a = -3. After substituting these values in the distance formula we get: D =√[(4-(-2))2 + (-3-1)2) = √((4+2)2 + (-3-1)2] = √(62 + (-4)2) = √(36 + 16) = √52 = 7.21 units. Therefore, using the distance formula, we found that the length of the line segment with coordinates (-2, 1) and (4, –3) is 7.21 units.
