What shape is formed by all points equidistant from a given point?a)Tr...
A circle is defined as the set of all points that are equidistant from a given point (the center).
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What shape is formed by all points equidistant from a given point?a)Tr...
Understanding Equidistant Points
When we talk about all points that are equidistant from a given point, we are describing a specific geometric shape. Let’s explore what this means.
Definition of Equidistant
- Equidistant refers to points that are the same distance away from a specific point, known as the center or focus.
Shape Formed
- The shape formed by all these equidistant points is a circle.
Why a Circle?
- A circle is defined as the set of all points in a plane that are at a fixed distance (the radius) from a central point (the center).
Characteristics of a Circle
- Center: The specific point from which all other points are measured.
- Radius: The constant distance from the center to any point on the circle.
- Uniform Distance: Every point on the circumference of the circle is the same distance from the center.
Conclusion
- Therefore, when you consider all points that are equidistant from a single point, you form a circle. This is distinct from other shapes like triangles, squares, or rectangles, which do not maintain a constant distance from a single point.
In summary, the correct answer is indeed option 'C', a circle, as it perfectly illustrates the concept of equidistance from a central point.