Line Segments

A line segment has two end points and it is a part of a line. Sides of a rectangle and triangle are some examples of line segment. A line segment has two end points and it is a part of a line. Sides of a rectangle and triangle are some examples of line segment.

• In this figure x, y are the two end points, and the line segment is` bar (XY)` .
• The length of the line segments xy would be written as xy. And the line segments have used the name as to be two end points xy.

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The midpoint of a line segment, AB given by the co-ordinates A(x1,y1) and B(x2,y2) is given by the formula shown below,

MidPoint (C)= ((x1+x2)/2,(y1+y2)/2)

For example, consider the line segment A(2,2) and B(8,10)

The midpoint of AB, C = ($\frac{(2+8)}{2}$ ,$\frac{(2+10)}{2}$)

= ($\frac{10}{2}$, $\frac{12}{2}$)

= (5, 6)

Therefore, the midpoint of the line segment AB is (5, 6)

The distance between two given points is called length of the line segment. The length of xy is represented as `bar (XY)`. The line segment length is calculated using formula for distance.

Length of `XY = sqrt((x2-x1)^(2)+ (y2-y1)^(2))`

Below are some example problems on line segment

Example 1: Using the distance formula, solve the length of the line segment between the two end points. End points are M = (6, 2), N = (5, 4)

Solution: Line segment distance formula, MN= `sqrt ((x2-x1) ^ (2) + (y2-y1) ^(2)`

x₁=6 y₁= 2 x₂=5 y₂=4

MN = `sqrt ((5-6) ^ `

MN = `sqrt((-1) ^ `

MN = `sqrt (1+ 4)`

MN = `sqrt (5)`units

Example 2: Find the mid point between the two points (-4, -1), (5, 2)

Solution: Midpoint = `"(x1+x2) /2 `

Substitute (x1, y1) = (-4, -1) and (x2, y2) = (5, 2)

Midpoint = `((-4+5) /2), ((-1+2) /2)`

= `(1/2), (1/2)`

The mid point of the two points is` (1/2), (1/2)`