Find the Length of Line Segments

To find the length of a line segment, given the coordinates of its endpoints, we can use two methods.

 

Example

Find the length of the line segment AC whose endpoints are at:

 

A(-5, -3) and C(3, -3).

 

Method 1

Plot the points and count the squares.

This is a good method if you have time to do it and paper and pencil to hand!

 

 

AC is 8 units long. Just write 8

 

Method 2

If you don't have the time to plot the coordinates, this method is the best!

 

Subtract the relevant coordinates.

The x-coordinates of the endpoints of vertical lines will be the same.

The y-coordinates of the endpoints of horizontal lines will be the same.

 

A is at (-5, -3) and C is at (3, -3).

 

The line AC is horizontal because the y-coordinates are both -3.

 

Subtract the x-coordinates:  -5 - 3 = -8 or 3 - -5 = 8.

Ignore the sign:  -8 or 8 means a length of 8 units. Just write 8.

 

For vertical lines, we would subtract the y-coordinates.

 

Let's give it a try in some questions now.