# Two Distance Formulas???

• Jan 14th 2007, 09:50 AM
symmetry
Two Distance Formulas???
I know there are two distance formulas, right?

Formula A is D = rt.

Formula B is the long formula used to find the distance between two points on the xy-plane, right?

MY QUESTION:

Why do we call BOTH the distance formula if they are used for TWO different reasons?
• Jan 14th 2007, 10:02 AM
ThePerfectHacker
Quote:

Originally Posted by symmetry

Why do we call BOTH the distance formula if they are used for TWO different reasons?

That is typical in math. One term can mean a myraid of meanings. For example, tangent can be....

1)A tangent line to a circle.

2)The trigonometric tangent function.

3)The Derivative, in Calculus.

....
• Jan 14th 2007, 10:10 AM
anthmoo
Formula A is the real distance one, like the one in your car. It does not depend on direction, only how fast you've been going and how long far.

Formula B, often stated as s=ut+(1/2)at^2, is the one that uses displacement from a point. Displacement is a vector quantity so it depends what direction your going in but.

Condense it...

Distance is how far you've travelled relative to pretty much nothing.

Displacement is how far you are away from a certain point.

Wikipedia shows this well...

EDIT: Oh wait..was he talking about mathematical or more physics here?
**EDIT: Oh well similar meanings, im guessing ^_^
• Jan 14th 2007, 01:13 PM
symmetry
Ok
I was not talking about displacement. Displacement is a physics concept.
I am more interested in pure mathematics. Although, physics goes deep into math formulas and concepts, especially as used in astronomy.

I said there is a distance formula like this: D = rt

and then there is another distance formula used to measure the distance between (x,y) points on the xy-plane and this is what it looks like:

D = sqrt({x2 - x1)^2 + (y2 - y1)^2}).

Why are they BOTH called distance?

Thanks.
• Jan 14th 2007, 03:46 PM
topsquark
Quote:

Originally Posted by symmetry
I was not talking about displacement. Displacement is a physics concept.
I am more interested in pure mathematics. Although, physics goes deep into math formulas and concepts, especially as used in astronomy.

I said there is a distance formula like this: D = rt

and then there is another distance formula used to measure the distance between (x,y) points on the xy-plane and this is what it looks like:

D = sqrt({x2 - x1)^2 + (y2 - y1)^2}).

Why are they BOTH called distance?

Thanks.

Because they are both associated with the same concept: how far away something is. D = rt (by the way, as a Physicist I HATE the word "rate" used in this context) measures the distance travelled by an object moving at a constant "rate" of speed. The Pythagorean distance formula measures the distance between two points in space. If you have an object moving from point (x1, y1) to point (x2, y2) at a constant speed r (directed from point 1 to point 2) over a time t then you can even combine these formulas:
$\displaystyle \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = rt$

-Dan
• Jan 14th 2007, 05:07 PM
symmetry
ok
Dan,

Thanks for the information. It's good to know that you're a Physicist. I may come across math questions dealing with physics. I love the study of physics in relation to astronomy and amusement park thrill rides.