Question

question 10 of 10

which geometric object is defined as the set of all points in a plane that are equidistant from the two sides of a given angle?

a. bisector of an angle
b. parabola
c. hyperbola
d. circle

Explanation:

Analyze the geometric definition

The problem asks for the set of all points in a plane equidistant from the two sides of a given angle. By definition, the distance from a point to a line (or ray) is the length of the perpendicular segment from the point to that line.

Evaluate the options

• Bisector of an angle: Any point on the angle bisector is equidistant from the two rays forming the sides of the angle. Conversely, any point equidistant from the sides lies on the bisector.
• Parabola: The set of points equidistant from a fixed point (focus) and a fixed line (directrix).
• Hyperbola: The set of points where the absolute difference of distances to two foci is constant.
• Circle: The set of points equidistant from a single central point.

Determine the correct choice

The definition perfectly matches the bisector of an angle.

Answer:

• A. Bisector of an angle (Correct answer)
• B. Parabola
• C. Hyperbola
• D. Circle