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How do I find the location of a point based on distance from three fixed points?
Given any three fixed points (a, b, c) which locations are known, how would I get the coordinate of some arbitrary point (x) for which the distances from each fixed point is known?
I imagine it would have much to with where the circles (or spheres in 3 dimensions) would intersect.
(The circles drawn from a radius of the given distances.) I am just unsure how to go about this mathematically.
1 Answer
- The WolfLv 61 decade agoFavorite Answer
Let the three fixed points be (a₁,b₁,c₁), (a₂,b₂,c₂) & (a₃,b₃,c₃) and let the distances from an arbitrary point (x,y,z) be d₁, d₂ & d₃ respectively then using the distance formula you get three equations
d₁² = (x-a₁)² + (y-b₁)² + (z-c₁)²
d₂² = (x-a₂)² + (y-b₂)² + (z-c₂)²
d₃² = (x-a₃)² + (y-b₃)² + (z-c₃)²
now substitute your a,b,c & d values then expand and solve simultaneously for x,y,z
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