# Thread: finding the point of intesection of lines connecting 3 points

1. ## finding the point of intesection of lines connecting 3 points

if we have 3 points (all having +ve co-ordinates(>=0)) in X-Y co-ordinate system, then how can we find the co-ordinates of intesection of lines of minimum lenght which connect them?
I thought it could be the centroid of the trinagle formed by these point but it doesn't seem so . Can there be any other such property?
E.g for points (2,2) ,(1,1) and (2,1) , the requied point is
1.788675 1.211324

Thanks.

2. ## Re: finding the point of intesection of lines connecting 3 points

Originally Posted by pranay
if we have 3 points (all having +ve co-ordinates(>=0)) in X-Y co-ordinate system, then how can we find the co-ordinates of intesection of lines of minimum lenght which connect them?
I thought it could be the centroid of the trinagle formed by these point but it doesn't seem so . Can there be any other such property?
E.g for points (2,2) ,(1,1) and (2,1) , the requied point is
1.788675 1.211324

Thanks.
Question: are you minimizing the sum of the distances? If so, there is a very elegant solution of this problem in this book, pages 6-7. If you do the "Search Inside This Book", and search for "drilling three holes", you will at least get page 6, which contains most of the derivation. The mathematical derivation is on page 7.

3. ## Re: finding the point of intesection of lines connecting 3 points

Originally Posted by pranay
if we have 3 points (all having +ve co-ordinates(>=0)) in X-Y co-ordinate system, then how can we find the co-ordinates of intesection of lines of minimum lenght which connect them?
I thought it could be the centroid of the trinagle formed by these point but it doesn't seem so . Can there be any other such property?
E.g for points (2,2) ,(1,1) and (2,1) , the requied point is
1.788675 1.211324

Thanks.
you probably are asking for this http://en.wikipedia.org/wiki/Fermat_point