how do you find the distance between 2 points with known distances between other points

Asked Jul 10 '15 at 07:07

Active Jul 10 '15 at 07:16

Viewed 73 times

enter image description here

I am trying to determine the distance between i and j.

These nodes are all placed in a coordinate system.

things I know:

Does anybody know a way of doing this? Thanks

edited Jul 10 '15 at 07:16

Henry

asked Jul 10 '15 at 07:07

user250453

If you know the coordinates of $i,p,q$, you don't need to explicitly state that you know the distances $ip, iq,pq$. More importantly, though, are you working in two dimensions or more than two? Because in two dimensions there are only two different places $j$ can be with the given distances, while in higher dimensions there's a whole continuum. – Arthur Jul 10 '15 at 07:12
You may write equation of circles with centres at $p$ and $q$ with radiuses $qj$ and $pj$. $j$ is intersection of these. – Michael Galuza Jul 10 '15 at 07:13
It rather depends on if you know whether $i$ and $j$ are on the same side of the line $pq$ or on opposite sides. – Henry Jul 10 '15 at 07:17
Are there any restrictions? There might not always be enough information. For example in the image you gave point $j$ could have been on the other side of line connecting $p$ and $q$ and you would have got the same information. – Reactant Jul 10 '15 at 07:26

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