calculate the distance between 2 points

hi every one i want to calculate the distance between 2 points(p1 & p2), so which of the following equation choose to do that:-

d = (x(p1)-x(p2))^2+(y(p1)-y(p2))^2;

or

d = sqrt((x(p1)-x(p2))^2+(y(p1)-y(p2))^2);

or any one from the above equations

thanks

Answer 1

[Grzegorz Knor]

The common use distance formula is the second one:

d = sqrt((x(p1)-x(p2))^2+(y(p1)-y(p2))^2);

http://en.wikipedia.org/wiki/Distance

[Majid Al-Sirafi]

but whew i try first one

d = (x(p1)-x(p2))^2+(y(p1)-y(p2))^2; instead of second one

d = sqrt((x(p1)-x(p2))^2+(y(p1)-y(p2))^2);

i felt that is useful for me, can i use the first one???

thank you dear

[Grzegorz Knor]

Of Course you can use it, but you have to remember that it won't be an Euclidean norm.

There are a lot of distance function in mathematics, e.g.:

http://en.wikipedia.org/wiki/E-statistic

http://en.wikipedia.org/wiki/Hamming_distance

http://en.wikipedia.org/wiki/Levenshtein_distance

http://en.wikipedia.org/wiki/Chebyshev_distance

http://en.wikipedia.org/wiki/Canberra_distance

http://en.wikipedia.org/wiki/Lee_distance

[Jan]

I like the distance in the Minkowski space: http://en.wikipedia.org/wiki/Minkowski_distance

It can be *negative* with the obvious unexpected effects.

[Majid Al-Sirafi]

thank you dear friends for your advices

[Oleg Komarov]

Please accept this answer if you think it solved your question.

[Rob Comer]

The hypot function in MATLAB provides a more compact way to code the Euclidean distance that is equivalent algebraically, but less susceptible to overflow, and probably more efficient:

d = hypot(x(p1)-x(p2), y(p1)-y(p2));

[Majid Al-Sirafi]

thank you dear Rob

dear

after calculating the distance (d) between (p1 and p2), i want to change the distance (for example suppose that i found the distance 10 unit and i want to change it into 12, that means i must move the points according this changing so

by which equation can i do that

[Jan]

You can either move P1, or P2 or both. There is an infinite number of possible end positions. Which one do you prefer?

[Majid Al-Sirafi]

dear jan...my suggestion is as the following:-

find the difference between old distance(10) and new distance(12) which will be 2... then move each point by half of distance(1)

[Daniel Shub]

@majid, but in what direction?

[Majid Al-Sirafi]

one point to the left and another to the right

Answer 2

[Jan]

You can simply try it, if you are not familiar with the Euclidean Norm (hint: use this term to ask Google or WikiPedia):

Set the variables to coordinates, whichj have a known distance, e.g. [0,0] and [2,0].

[jaafar rashid]

are they norme and ecludian same??