# Thread: Distance formula...which one is right?

1. ## Distance formula...which one is right?

This is a basic question. Distance is defined mathematically by the square root of the squared difference between a and b. Then what do the expressions a-b and Ia-bI (absolute value) mean?

2. Originally Posted by nonintegral
This is a basic question. Distance is defined mathematically by the square root of the squared difference between a and b. Then what do the expressions a-b and Ia-bI (absolute value) mean?
The distance between two points $a~\&~b$ on a number line is $\left| {a - b} \right|$.

The distance between two points in a plane $(p,q)~\&~(r,s)$ is $\sqrt {\left( {p - r} \right)^2 + \left( {q - s} \right)^2 }$.

Does that help?

3. Originally Posted by Plato
The distance between two points $a~\&~b$ on a number line is $\left| {a - b} \right|$.

The distance between two points in a plane $(p,q)~\&~(r,s)$ is $\sqrt {\left( {p - r} \right)^2 + \left( {q - s} \right)^2 }$.

Does that help?

It helps a lot. Thanks.

4. Originally Posted by nonintegral
It's helping. I know that $\sqrt {\left( {a - b} \right)^2}$ is from the Pythagorean theorem. What I'm really not clear on is what $\sqrt {\left( {p - r} \right)^2 + \left( {q - s} \right)^2 }$ means.
I don't know what you mean about understanding?