Segments are one of the basics in geometry. You can use algebra to help measure distances between points (coordinates*) on a segment, measure a segment to determine the distance between points, and more! It's really quite simple.
Remember learning about absolute value? Well, here's where you will be using it again. The distance between any two points on a segment is the absolute value of the difference of the coordinates. Let's see what this looks like. 

Here's a segment, MN, and we want to find the distance between the two points. The coordinates are 3 and 9 so let's use our knowledge of absolute value. MN = M – N = N – M or MN = 3 – 9 = 9 – 3 = 6 So, the length or distance between M and N is 6. Easypeasy, lemonsqueasy! 

The Segment Addition Postulate


Segment Addition Postulate Next up is learning to find the distance/length of a segment. You use algebra to do this! (See? There WAS a reason for taking algebra before geometry!) Here are two common problems. The first one is strictly algebraic. Problem #1: B is between A and C, AC = 20 and BC = 12.4. Find AB. Yikes! What to do! 

Step 1: Set up your problem. What information do you know? You know that AC = 20. You also know that BC = 12.4. You also know that AB + BC = AC. So, let's write this as a problem. 

AC = AB + BC 

Step 2: Substitute numbers for the variables. Substitute what you know into your problem.


AC = AB + BC 20 = AB + 12.4 

AC = AB + BC 20 = AB + 12.4 12.4 12.4 7.6 = AB 

Step 3: Simplify. Solve the problem. Voila! Easypeasy, lemonsqueasy! 

The Segment Addition Property states that AC = AB + BC so by substituting the values you do know and then simplifying, you can find the missing value! 

Problem #2: N is between M and O. Find MO. Goodness! How do you do this one? Again, think of what you know from algebra and the Segment Addition Postulate. 

Step 1: Set up your problem. What information do you know? You know that MO = MN + NO. Looking at the graphic in the problem, you can see that MO = 6x. You also see that MN = 2x + 4. So, let's write this as a problem. 

MO = MN + NO 

Step 2: Substitute numbers for the variables. Substitute what you know into your problem.


MO = MN + NO 6x = (2x + 4) + 28 

MO = MN + NO 6x = (2x + 4) + 28 2x 2x 4x = 4 + 28 4x = 32 4 4 x = 8 

Step 3: Simplify. Solve the problem. 

Step 5: Go back and substitute. Now, go back and substitute the value for what the question is asking for. Yay! Easypeasy, lemonsqueasy! 

MO = 6x = 6 • 8 = 48 

©2016 Sherry Skipper Spurgeon for Geometry Bugs Me All Rights Reserved 
