Complete the two activities below to understand what object is formed by...
(1) The set of all points in a plane that are a given distance from a point in the plane.
(2) The set of all points in a plane that are equidistant from two points in the plane.

In Chapter 10, you will learn that another name for the set of all points satisfying a certain condition is locus. Therefore, you could say that the object formed by the red points in...
(1) is the locus of points in a plane that are a given distance from a point in the plane.
(2) is the locus of points in a plane that are equidistant from two points in the plane.