First, create a visual representation of the line with the collinear points:
A B C
•—————-•—————•
We are given that BC=8.5 and AC=13.2, and we must find the length of segment AB. Because line segment AB is unknown, we will denote it as “x.”
Looking at the construction of the line segment, we can see that AC is the whole length of the segment, and BC is is fraction of the segment. So, we can create the following equation:
x+8.5=13.2
We know that segment AB added to segment BC must sum up to 13.2. So, we can solve for x:
Subtract 8.5 from both sides:
x=13.2-8.5
x=4.7
This means the length of segment AC is 4.7. We can plug this value back into the equation to make sure it is correct:
4.7+8.5=13.2
13.2=13.2
So, the length of segment AB is 4.7.