Question

question 5 of 10

which of the following best describes a line?

a. the set of all points in a plane that are equidistant from three points
b. the set of all points in a plane that are equidistant from a given point and a given line
c. the set of all points in a plane at a given distance from a given point
d. the set of all points in a plane that are equidistant from two points

Explanation:

Analyze the geometric locus definitions

Using the Locus of Points and Geometric Definitions knowledge points, we evaluate each option to find which one describes a line (specifically, the perpendicular bisector, which is a line).

• Option A describes a set of points equidistant from three points. If the three points are non-collinear, this set contains at most one point (the circumcenter).
• Option B describes a parabola. Using the Parabola Definition knowledge point, the set of points equidistant from a point (focus) and a line (directrix) is a parabola.
• Option C describes a circle. Using the Circle Definition knowledge point, the set of points at a given distance from a given point is a circle.
• Option D describes a perpendicular bisector. The set of all points in a plane equidistant from two given points forms a straight line.

Answer:

• A. The set of all points in a plane that are equidistant from three points
• B. The set of all points in a plane that are equidistant from a given point and a given line
• C. The set of all points in a plane at a given distance from a given point
• D. The set of all points in a plane that are equidistant from two points (Correct answer)