The locus of points that are a fixed distance from a given point describes which geometric shape?

The locus of points that are a fixed distance from a given point describes a circle. This is because a circle can be defined as the set of all points in a plane that are at a constant distance, known as the radius, from a central point called the center.

For instance, if you take any point that is equidistant from a specific central point, and if you move around that point maintaining the same distance, you will trace out the shape of a circle. This fundamental property of circles is essential in geometry and underlies many concepts related to distance and symmetry.

Other shapes listed do not represent the same characteristic. A line describes a set of points extending infinitely in two directions without curvature and does not maintain a constant distance from any point. A polygon consists of a finite number of straight line segments connected to form a closed shape, which does not have the uniform distance characteristic of a circle. An ellipse is a more complex shape defined by two focal points, where the sum of the distances from any point on the ellipse to these two foci is constant, which is different from the definition of a circle. Thus, the defining feature of a circle makes it the correct answer in this context.