Question

Which geometric figure consists of the set of all points in a plane that are the same distance from a given point?

Answer 1

An arc, a circle and a sphere describe a geometric figure consisting of the set of points in a plane that are the same distance from a given point.

An arc is any two connected sections of the circumference of a circle. Whereas an arc consists of the set of points in a plane that are the same distance from a given point it does not consist ALL the points.

A circle is a simple closed shape in consisting of the set of all points in a plane that are at a given distance from a given point, called the centre of the circle. A circle is a 2-dimensional figure and thus does not contain set of points in the 3-dimensional plane. Hence a circle does not consist ALL the points in a plane that are at a given distance from a given point.

A sphere is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball. Like a circle, which geometrically is an object in two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance, r, from a given point, but in three-dimensional space. This distance, r, is the radius of the sphere, and the given point is the center of the sphere.

Thus, the sphere consists of the set of ALL points in a plane that are the same distance from a given point.

Answer 2

Answer:

An arc, a circle and a sphere describe a geometric figure consisting of the set of points in a plane that are the same distance from a given point.

An arc is any two connected sections of the circumference of a circle. Whereas an arc consists of the set of points in a plane that are the same distance from a given point it does not consist ALL the points.

A circle is a simple closed shape in consisting of the set of all points in a plane that are at a given distance from a given point, called the centre of the circle. A circle is a 2-dimensional figure and thus does not contain set of points in the 3-dimensional plane. Hence a circle does not consist ALL the points in a plane that are at a given distance from a given point.

A sphere is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball. Like a circle, which geometrically is an object in two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance, r, from a given point, but in three-dimensional space. This distance, r, is the radius of the sphere, and the given point is the center of the sphere.

Thus, the sphere consists of the set of ALL points in a plane that are the same distance from a given point.

Step-by-step explanation: