Length of a Line Segment Formula

Length of a line segment formula :   
                                             

Length of line segment is the distance between two coordinate points in a co ordinate plane. It is showed by the units of length .

Suppose there are two points (x₁,y₁) and (x₂,y₂) is

                                D² = (y₂-y₁)² + (x₂-x₁)²

                                This formula is simply a use of Pythagoras' Theorem. 

If the line segments is exactly vertical or horizontal, the formula above will still work fine, but there is an easier way. For a horizontal line, its length is the difference between the x-coordinates. For a vertical line its length is the difference between the y-coordinates. In the figure above make a vertical and horizontal line and verify this for yourself.     

Example on Length of a Line Segment Formula :

problem: Find the distance between two points (length of line segment between two points) in coordinate plane (3,5) , (0,1)

                                       Given two points are (x₁,y₁)= (3,5)

                                                          and (x₂,y₂) = (0,1)

                     There fore

                                                            D² = (y₂-y₁)² + (x₂-x₁)²

                                                            D² =  (1-5)² + (0-3)²

                                                            D² =   (-4)²  + (-3)²

                                                            D² =  16 + 9

                                                            D² = 25

                                                        =>D = √25 = 5

Therefore the length of line segment between the given points is 5 units

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Example on Length of a Line Segment Formula :

Problem: The length of line segment is 13 between the points (1,0) and (a,5) . Find a?

                              Given the length of line segment is 13

                               The points(x₁,y₁)= (1,0)

                               and (x₂,y₂) is (a,5)

                      There fore

                               D² = (y₂-y₁)² + (x₂-x₁)²

                              13²=(a-1)² + (5-0)²

                         => 169= (a-1)² + 5₂

                         => (a-1)² + 25= 169

                         => (a-1)² = 169-25 = 144

                         => (a-1)² = 144

                         => (a-1)²= √144

                         => (a-1)=12

                         => a= 12+1 =13

     The missing value a is 13

Conclusion on Length of a Line Segment Formula :

                                            Finally in this way we can calculate the length of line segment by the formula

  D² = (y₂-y₁)² + (x₂-x₁)²  where

D  is Distance(Length of line segment)

(x₁,y₁) is one point in coordinate plane

(x₂,y₂) is other point in coordinate plane

The length of line segment is denoted by units specified for the points in coordinate plane.

 We can also find the missing points the coordinate axis if the length of line segment is given and one of the points is given. This part of example is shown in example 2 .