trying to find Coordinates of point D
I have coordinates for A, B and C . I also have distance to D from points A, B and C.
I'm going to call distances X distance from A, Y distance from B and Z distance from C.
How can I find D's coordinates on 3D place given all those information.
Thank you in advance!
Sorry for simplifying it.
[Math] Finding Coordinates of a Point in 3D with Known Distances From 3 Other Points.
3dgeometry
Best Answer
You need to find the coordinates of a point $D(x,y,z)$. Then, you need to make three equations (in order to find the three variables $x$, $y$ and $z$. Solve the system of equations and you´ll get the value of $x$, $y$ and $z$.
Construct each equation by the information given, for instance:
$$\tag {1} d_{AD}=\sqrt {(x-x_A)^2+(y-y_A)^2+(z-z_A)^2}$$
If $d_{AD}$ is the distance from $A(x_A,y_A,z_A)$ to $D(x,y,z)$
The same thing with:
$$\tag {2} d_{BD}=\sqrt {(x-x_B)^2+(y-y_B)^2+(z-z_B)^2}$$ $$\tag {3} d_{CD}=\sqrt {(x-x_C)^2+(y-y_C)^2+(z-z_C)^2}$$
Solve the system of the equations (1), (2) and (3) and find the values of $x$, $y$ and $z$