Question

James defines a circle as "the set of all the points equidistant from a given point." His statement is not precise enough because he should specify that

a circle includes its diameter
the set of points is in a plane
a circle includes its radius
the set of points are collinear

Answer 1

The statement provided by James about a circle needs clarification is The set of points is in a plane is correct option b.

James's definition of a circle as the set of points equidistant from a given point needs clarification. A circle indeed comprises points in a plane, emphasizing its two-dimensional nature. It's crucial to specify this plane aspect as circles exist in 2D space, not extending into three dimensions.

Moreover, a circle encompasses all points equidistant from its center, including its radius and diameter. By defining the plane and acknowledging the inclusion of the radius and diameter, the definition becomes more precise.

A circle is defined as the set of all points in a plane that are equidistant from a single fixed point, called the center. This definition encompasses all points lying on the circle's perimeter, including its radius and diameter, within the same plane. Therefore, option B is the most accurate clarification for James's statement.

complete the question

James defines a circle as "the set of all the points equidistant from a a given point" His statement is not precise enough because he should specily than

A)a circle includes its diameter

B)the set of points is in a plane

C)a circle includes its radius

D)the set of points are collinear

Answer 2

Answer: choice B) the set of points is in a plane

Reason:

If we considered points in 3D space equidistant from a fixed point, then we describe a sphere.

If we restrict all the points to a single plane, then we get a circle.

A plane is a flat surface that does not have any curved portions. Think of a table surface as one example.