Question

which of the following is the best definition of a circle? a. a plane figure similar to a hexagon b. a polygon with curved sides c. the collection of all points in a plane that are the same distance from a given point d. the collection of all points in a plane that are the same distance from a given line

Explanation:

• Option A is incorrect: a circle is not similar to a hexagon, as they have fundamentally different shapes (curved vs. straight-sided).
• Option B is incorrect: a polygon is defined as a closed figure with straight sides, so a shape with curved sides cannot be a polygon.
• Option C is correct: this is the standard mathematical definition of a circle, where the given point is the center, and the fixed distance is the radius.
• Option D is incorrect: the set of points equidistant from a given line is a pair of parallel lines (a parabola is the set of points equidistant from a line and a point, not all points equidistant from a single line).

Answer:

C. The collection of all points in a plane that are the same distance from a given point