Line Segment Distance

Introduction to line segment distance:
Line segment are one of the basis for mathematics. Line segment are denote by using the end points. There are two end points for the line segment. The two end endpoints given are having some conditions. The condition is the line segment should not exceed the line. The line segment is represented using the letters the are alphabet.

Explanation for Line Segment Distance

The distance of the line segment can be represented as the following diagram,

The formula for representing the distance of the line segment is,

Distance = AB = `sqrt((x_(1)-x)^2)+(y_(1) -y)^2`  

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Example Problem for Line Segment Distance

Problem 1: Find the line segment for the given function, where A(2, 4) and B(3, 6).

Solution:

Step 1: Write the formula for the distance of the line segment.

Distance = AB = `sqrt((x_(1)-x)^2)+(y_(1) -y)^2`

Step 2:  The value of  x = 2, y = 4 and x1 = 3, y1 = 6.

Step 3: Substitute the given values in the formula, we get,

AB = `sqrt((3-1)^2)+(6 -4)^2`

AB=`sqrt(2^2+4^2)`

AB=`sqrt(4+16)`

AB=`sqrt(20)` units.

Problem 2: Find the line segment for the given function, where A(3, 6) and B(4, 8).

Solution:

Step 1: Write the formula for the distance of the line segment.

Distance = AB = `sqrt((x_(1)-x)^2)+(y_(1) -y)^2`

Step 2:  The value of  x = 3, y = 6 and x1 = 4, y1 = 8.

Step 3: Substitute the given values in the formula, we get,

AB = `sqrt((4-3)^2)+(8 -6)^2`

AB=`sqrt(1^2+2^2)`

AB=`sqrt(1+4)`

AB=`sqrt(5)`

Line Segment Distance Problem for Equation

Problem 1: By using the given functions find the equation for the line segment . AB=4, A(2,4) and B(x,6).

Solution:

Step 1: Write the formula for the distance of the line segment.

Distance = AB = `sqrt((x_(1)-x)^2)+(y_(1) -y)^2`

Step 2:  The value of  x = 2, y = 6 and x1 = 4, y1 = x. and AB=4

Step 3: Substitute the given values in the formula, we get,

4 = `sqrt((4-2)^2)+(x -6)^2`

4=`sqrt(2^2+(x-2)^2)`

4=`sqrt(4+(x-2)^2)`

4=2+  `sqrt((x-2)^2)`

`6=``(x-2)^(2)`

This is the required equation for the given problem.