# Distance formula...which one is right?

• Aug 8th 2009, 12:12 PM
nonintegral
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?(Headbang)
• Aug 8th 2009, 12:25 PM
Plato
Quote:

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 $\displaystyle a~\&~b$ on a number line is $\displaystyle \left| {a - b} \right|$.

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

Does that help?
• Aug 8th 2009, 12:57 PM
nonintegral
Quote:

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

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

Does that help?

It helps a lot. Thanks.
• Aug 8th 2009, 01:03 PM
Plato
Quote:

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

I don't know what you mean about understanding?