# given distances to 3 known points 2d, find the 4th point

Lets say you have three points in $2D$, which are non-collinear: $a$, $b$ and $c$.

How can you find a $4$th point, when you have the distance from the $4$th point to $a$, $b$ and $c$ ?

-

## migrated from stackoverflow.comDec 22 '11 at 23:30

This question came from our site for professional and enthusiast programmers.

The formula for distance is [(x-x1)^2+(y-y1)^2+(z-z1)^2]^(1/2). Just plug in your known points and you have three linear equations in three variables. –  nw. Dec 22 '11 at 22:37
Is the fourth point to be in the same plane as the other three? Then for almost all combinations $(d_1,d_2,d_3)$ of distances, there will not be such a fourth point. –  André Nicolas Dec 22 '11 at 23:53