Which geometric object is defined as the set of all points in a plane at a given distance from a given point?
A. Circle
B. Line
C. Line segment
D. Parabola
Answer (1)
A circle is defined as the set of all points equidistant from a center.
A line and a line segment are straight figures and do not fit the definition.
A parabola is a U-shaped curve with a focus and directrix, not a fixed distance from a single point.
The geometric object that matches the definition is a circle: C i rc l e .
Explanation
Analyze the problem The question asks us to identify a geometric shape based on its definition: the set of all points in a plane at a fixed distance from a given point. Let's analyze each option to see which one fits this definition.
Analyze the options A. Circle: A circle is defined as the set of all points in a plane that are equidistant from a central point. This perfectly matches the given definition. B. Line: A line is a straight, one-dimensional figure extending infinitely in both directions. It doesn't involve a fixed distance from a single point. C. Line segment: A line segment is a part of a line bounded by two endpoints. Like a line, it doesn't fit the definition. D. Parabola: A parabola is a U-shaped curve defined by a focus point and a directrix line. Points on a parabola are equidistant from the focus and the directrix, which is different from the given definition.
Identify the correct answer Based on the definitions, a circle is the only geometric object that fits the description of being the set of all points in a plane at a given distance from a given point (the center).
State the final answer Therefore, the correct answer is OA. Circle.
Examples
Circles are fundamental in many real-world applications. For example, the wheels on vehicles are circular, allowing for smooth and efficient movement. The circular shape ensures a constant distance from the center (the axle) to the ground, providing stability. Similarly, circular gears are used in machinery to transmit rotational motion, and the circular design ensures consistent and predictable performance.
