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.

AC is 8 units long. Just write 8.

This method is fine if you have paper and time, and the coordinates are small.

 

 

Method 2

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 subtract the y-coordinates.