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Definition

The definition of equidistant is simple: a set of points that are at the same distance from a specific point or set of points. In other words, the distance between any point in the set and the specific point or set of points is constant. This distance is called the equidistant distance or the radius of the equidistant set.

Equidistant can be used in one, two, or three dimensions, depending on the number of points involved. In one dimension, the equidistant set is a pair of points that are equidistant from a single point. In two dimensions, the equidistant set is a circle that is equidistant from a single point. In three dimensions, the equidistant set is a sphere that is equidistant from a single point.

Examples

Equidistant can be used in various mathematical fields, including geometry, algebra, and trigonometry. Here are ten examples of its use:

1. In geometry, the equidistant set is used to define a circle. A circle is a set of points that are equidistant from a center point. The radius of the circle is the distance between the center point and any point on the circle.
2. In algebra, the equidistant set is used to solve equations. For example, if you have two points on a line and you want to find the point that is equidistant from both points, you can use the midpoint formula: (x1 + x2)/2, (y1 + y2)/2.
3. In geometry, the equidistant set is used to define a sphere. A sphere is a set of points that are equidistant from a center point in three dimensions. The radius of the sphere is the distance between the center point and any point on the sphere.
4. In trigonometry, the equidistant set is used to define a unit circle. A unit circle is a circle with a radius of one that is centered at the origin of a coordinate plane. The unit circle is used to define trigonometric functions such as sine, cosine, and tangent.
5. In geometry, the equidistant set is used to define an ellipse. An ellipse is a set of points that are equidistant from two points, called foci. The distance between the foci is called the focal distance.
6. In algebra, the equidistant set is used to find the equation of a perpendicular bisector. A perpendicular bisector is a line that passes through the midpoint of a line segment and is perpendicular to the line segment. The equation of a perpendicular bisector is y = mx + b, where m is the slope of the line and b is the y-intercept.
7. In geometry, the equidistant set is used to define a parabola. A parabola is a set of points that are equidistant from a fixed point, called the focus, and a fixed line, called the directrix.
8. In trigonometry, the equidistant set is used to define the six trigonometric functions. The six trigonometric functions are sine, cosine, tangent, cosecant, secant, and cotangent. These functions relate the ratios of the sides of a right triangle to the angles of the triangle
9. In geometry, the equidistant set is used to define a hyperbola. A hyperbola is a set of points that are equidistant from two fixed points, called the foci. The distance between the foci is called the distance between the foci.
10. In algebra, the equidistant set is used to find the equation of a circle. If you have the center point and a point on the circle, you can use the distance formula to find the radius of the circle. Then, you can use the equation of a circle, which is (x – h)² + (y – k)² = r², where (h, k) is the center point and r is the radius.

FAQ

Q: What is the difference between equidistant and equilateral? A: Equidistant refers to a set of points that are at the same distance from a specific point or set of points, while equilateral refers to a shape that has all sides of equal length.

Q: What is the equidistant point? A: The equidistant point is the point that is equidistant from two or more points.

Q: How do you find the equidistant point between two points? A: To find the equidistant point between two points, you can use the midpoint formula: (x1 + x2)/2, (y1 + y2)/2.

Q: What is the equidistant line? A: The equidistant line is a line that is equidistant from two or more points.

Q: What is the equidistant distance? A: The equidistant distance is the distance between any point in the set and the specific point or set of points.

Quiz

1. What is equidistant? A. A set of points that are at the same distance from a specific point or set of points. B. A shape that has all sides of equal length. C. A set of points that are at a different distance from a specific point or set of points.
2. What is the equidistant set in one dimension? A. A pair of points that are equidistant from a single point. B. A circle that is equidistant from a single point. C. A sphere that is equidistant from a single point.
3. What is the equidistant set in two dimensions? A. A pair of points that are equidistant from a single point. B. A circle that is equidistant from a single point. C. A sphere that is equidistant from a single point.
4. What is the equidistant set in three dimensions? A. A pair of points that are equidistant from a single point. B. A circle that is equidistant from a single point. C. A sphere that is equidistant from a single point.
5. What is the equation of a perpendicular bisector? A. y = mx + b B. (x – h)² + (y – k)² = r² C. (x1 + x2)/2, (y1 + y2)/2.
6. What is a hyperbola? A. A set of points that are equidistant from a fixed point, called the focus, and a fixed line, called the directrix. B. A set of points that are equidistant from two points, called foci. C. A set of points that are equidistant from a center point.
7. What is the distance between the foci of a hyperbola called? A. Focal distance. B. Radius. C. Circumference.
8. What is the equidistant set used for in geometry? A. To define a hyperbola. B. To find the equation of a circle. C. To find the equation of a line.
9. What is the equidistant point? A. The point that is equidistant from two or more points. B. The point that is equidistant from three or more points. C. The point that is equidistant from a single point.
10. How do you find the equidistant point between two points? A. Use the midpoint formula. B. Use the distance formula. C. Use the equation of a circle.

Answers:

1. A
2. A
3. B
4. C
5. A
6. B
7. A
8. A
9. A
10. A