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The set of all points a given distance from a center point is a circle. The given distance is the radius, and the given point is the center.

In 3 dimensional space, the set would be the surface of a sphere.

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What is the set of points in a plane at a fixed distance from a given point?

CIRCLE


What is the locus of all points that are a fixed distance from a given point?

triangle


What name is given to the set of all points in a plane that are the same distance from a given fixed point?

A circle.


A compass draws all points a given distance from a fixed point thereby creating a locus of points for a circle?

True


What is the locus for a point and fixed distance?

The locus of a point at a fixed distance from a given point is a circle. The center of the circle is the fixed point, and the radius is the fixed distance. Each point on the circle is equidistant from the center, representing all possible locations of the point at that specific distance.


The set points in space that are a given distance from a given point is?

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.


Which is a solid bounded by the set of all points at a given distance from a given point?

A sphere is a solid bounded by the set of all points at a given distance from a given point.


The set of all points in a plane that are the same distance from a fixed point?

This set of points forms a circle with the fixed point as its center.


A set of points that are ALL THE same distance from a given point?

The set of all points a given distance from a center point is a circle. The given distance is the radius, and the given point is the center. Or, in 3 dimensional space, a sphere.


What is the mathematical definition of a circle?

A circle is the set of all points in a plane that are a given distance (or a fixed distance) from another point. Take a plane, and then pick any point on it. Then pick a distance from that point you picked and connect all the points that are that distance from your fixed point. That will describe the circumference of a circle. Another idea is to take a plane, pick any point, and then take a compass and put the point of that instrument on that point you picked. Then set a distance on the compass and draw a circle. That circle will be that set of all points a fixed distance from the original point you picked. (A string will work as well as a compass if that string is not stretched to draw the circle.)


A collection of points in the plane whose distance from fixed point is constant?

That's a circle. The "fixed point" is the center of the circle, and the constant distance is its radius.


What is the locus of points at a given distance from a given point?

A circle