## Making Connection Between Distance and Absolute Value

We have learned about the distance formula and we also have discussed how to get the distance between two points given their coordinates.  In this post, we are going to explore a simpler concept: getting the distance between two points on the number line.

Suppose we want to get the distance between two p0ints on the number line whose coordinates are integers, we can just do it by counting. In the figure below, the distance from $0$ to $5$ is $5$, and the distance from $5$ to $9$ is $4$.

image via nctm illuminations

It is also obvious that we can get the distance by subtraction: $5-0=5$ and $9-5=4$.  It is clear that if we let $a$ be the larger integer, and $b$ be the smaller, then the distance can between the two integers is $a-b$. It is also clear that this formula applies to non-integral coordinates.  » Read more