Finding Distances on a Number Line

Finding Distances on a Number Line

 

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The distance between two points on a number line is the absolute value of the difference between the locations of the two points. If that seems a little complicated, let’s take it step by step. First, you need to identify the two points. As an example, let’s say our first point is located at -2 and our second point is located at 5 on this number line:

 

Now, we can find the distance by plugging in our points:

 

Distance = |5 − (-2)| [Remember that subtracting a negative is the same as adding]

Distance = |5 + 2|

Distance = |7|

Distance = 7

  So the distance between Point A (-2) and Point B (5) is 7 units. Notice that if you put the points in the opposite order, you would get the same answer:  

Distance = |-2 − 5|

Distance = |-7|

Distance = 7

 

The important thing to remember is that you take the absolute value of the difference between the two points' values. (If you need a review of absolute value, we’ve got you covered here.) We use absolute value because distance is a measure of how far apart two points are, and it should always be a positive value. (Think about it: could two things ever be -2 feet apart?) This gives you the straight line distance between the two points, ignoring direction.

 

Let's look at another example. Say one point is at 7 and the other is at -4.

 

Distance = |-4 - 7|

Distance = |-11|

Distance = 11

 

The distance between the point at 7 and the point at -4 is 11 units.