Given three collinear points on a line: A, B, and C. Pay close attention to the order. The total line segment is AC, since A is the starting point, B is some point on AC, and C is the endpoint. Given that AC=20, we now know that value is the total segment length from point A to C. We are also given that segment AB=12. We need to know the length of segment BC. Let’s form the following equation:
AB+BC=AC
• We know that from the segment addition postulate (which states adjacent segments can be added), the length of segment AB and BC total the overall segment length of AC. We are also told that AC=20, so 20 can be substituted in for AC since they are equal:
AB+BC=20
• With this, we are also told that segment AB is 12, and they have an equal relationship so they too can be substituted:
(12)+BC=20
• We set up this equation because we know that two segment sections sum up to 20, since A is the starting point, C is the endpoint, and B is somewhere between those two points. Now, we solve for segment BC using inverse operations of equality:
(12)-(12)+BC=20-(12)
• We want to isolate BC, so we must subtract 12 from both sides to cancel it out on the left and combine it with the like constant term on the right. We did this because 12-12=0, thus BC is now by itself.
BC=8
• We know that segment BC is equal to eight, so let’s input it back into the original equation to assure that both segment sections sum up to 20. All we really did was subtract 12 from 20 to find the difference (the value that adds to 12 to sum up to 20).
(12)+(8)=20
Therefore, BC=8.
BC could also be 12, which would make AB=8.
Answers: 8, 12