问题
If I have three points A, B, C and I know the distances between them and A is at 2D coordinates {0,0} and B is at {ab,0}, then what would be the formula to find the coordinates of the point C?
回答1:
The point {cx, cy} has to solve two equations:
cx^2+cy^2==ac^2 && (cx-ab)^2+cy^2==bc^2
=> cx^2-(cx-ab)^2==ac^2-bc^2
=> 2*cx*ab==ac^2-bc^2+ab^2
=> cx = (ac^2-bc^2+ab^2)/(2*ab)
=> cy = +/- sqrt(ac^2-cx^2) iff ac^2-cx^2 > 0
=> cy = 0 iff ac^2-cx^2 = 0
=> no solution else
There are either two points which both have the desired distances. But based on ac^2-cx^2 there may also be only one solution or none at all.
回答2:
If you don't place any further restrictions to the distances, your question is equivalent to "how to find the intersection of 2 circles":
http://mathworld.wolfram.com/Circle-CircleIntersection.html
Therefore, as Howard pointed out, there will be 0, 1, or 2 intersections points fulfilling the conditions you placed.
回答3:
You can use the distance formula (basically Pythagorean theorem) to find the distance between any two points on a coordinate plane.
http://www.purplemath.com/modules/distform.htm
来源：https://stackoverflow.com/questions/5370356/calculate-coordinates-of-a-point-with-given-distances-to-two-other-points