Boris B. answered 07/22/19
Expert Mechanical Design Engineer, (English-Russian)
In 1D, where each point is represented by one single number, it would only be possible to find the 3rd point, equidistant to two original points. If you imagine the two points on a line, the third point would then just be the center of those two points, which also happens to be the mean of those two points.
For three points, you would require a 2D space, i.e. each point must be a vector of length two: so basically an (x, y) coordinate pair.
Create a plane thru your 3 points of interest. Create a sketch thru these 3 points.
If you did have (x,y) coordinates for three unique points, they would form a triangle, and the equidistant position (i.e. your fourth point) is called the circumcenter, and it found by finding the center of each of the sides of the triangle, then drawing a line through each, which is perpendicular to its corresponding side of the triangle. These three lines will cross at the circumcenter - and it is not necessarily inside the triangle!