In three dimensions, the solid defined as being bound by the set of points at a given distance form a point is a sphere. In two dimensions, the figure defined as being bound by the set of points at a given distance from a point is a circle. In one dimension, a line segment is bound by the two points at a given distance from a point.
6.8
A set of all points is how various shapes are made in geometry. Lines are sets of points, and so are surfaces. Circles are sets of all points that are a fixed distance from a central point. All geometric shapes are made from sets of all points.
A sphere is a solid bounded by the set of all points at a given distance from a given point.
The point that is equal distance from the endpoints of a line segment is the midpoint.
A globular sphere has all points at the same distance from an interiocenter point.
A circle or a sphere
A Sphere.
That's a figure called a "circle". The given distance is the circle's radius, and the point is its center.
A sphere
circle
The question is ambiguous. Is the"single" point fixed or floating?
A circle
Sphere
In three dimensions, the solid defined as being bound by the set of points at a given distance form a point is a sphere. In two dimensions, the figure defined as being bound by the set of points at a given distance from a point is a circle. In one dimension, a line segment is bound by the two points at a given distance from a point.
They are called equidistant points and form points on a sphere for a solid or a circle on a plane figure.
Sphere