Line Segment Formula

A straight line which links two points without extending beyond them. Then the two end points are foundd out using the distance formula it is known as line segment formula.

       If the line has ends it would be called a "Line Segment". The distance formula is the formula for finding the length of the line segment. The line segment AB links the points A and B. The points A and B are called the 'endpoints' of the segment.

 

Line segment formula from two points

 

The length of the line segment:   The difference between two endpoints is called the length of the line segment . The length of the line segment is indicated with an overbar.

For example:

                                           

The length of the line segment XY is written as `bar (XY)` .

The length of line segment are calculated using distance formula. The line segment are two end points, the end points have x and y coordinates. Using two end points we find length of the line segment. X(x1,y 1) and Y(x 2,y 2). Distance between two end points are referred to as line segment formula.The line segments mid point also find using using mid point formula. The distance are of line segment are denoted by overbar.

         Line segment formula    XY = `sqrt( (x_2-x_1)^2 + (y_2 - y_1)^2`

 

 

Examples of line segment formula

 

Ex 1:    Find the distance between two end points using line segment formula. X(3,2) Y(4,5)

Solution:   Line segment formula    `bar(XY)` =  `sqrt( (x_2-x_1)^2 + (y_2 - y_1)^2`      where,  x1=3    y1= 2   x2=4    y2=5

                                                            XY = ?(4-3)2 + (5-2)2

                                                            XY = ?(1)2 + (3)2

                                                            XY = ?1+ 9

                                                            XY = ?10 units

 

Ex 2: Find the the distance using line segment formula  the end points are A(3,7) B(4,2)

Solution:   Line segment formula    `bar (AB)`  =  `sqrt( (x_2-x_1)^2 + (y_2 - y_1)^2`

                                                         x1=3    y1= 7   x2=4    y2=2

                                                            AB = ?(4-3)2 + (2-7)2

                                                            AB = ?(1)2 + (-5)2

                                                            AB = ?1+ 25

                                                            AB  = ?26 units

Ex 3:Find the the distance using line segment formula  the end points are P(0,2) Q(6,5)

Solution:                Line segment formula   `bar(PQ)`   =  `sqrt( (x_2-x_1)^2 + (y_2 - y_1)^2`

                                                         x1=0    y1= 2   x2=6    y2=5

                                                            PQ = ?(6-0)2 + (5-2)2

                                                            PQ = ?(6)2 + (3)2

                                                            PQ = ?36+ 9

                                                            PQ  = ?45 units