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Given two points A and B in the three dimensional space what is the set of points equidistant from A and B?
A plane is the set of all points in 3-D space equidistant from two points, A and B. If it will help to see it, the set of all points in a plane that are equidistant from points A and B in the plane will be a line. Extend that thinking off the plane and you'll have another plane perpendicular to the original plane, the one with A and B in it. And the question specified that A and B were in 3-D space. Another way to look at is to look at a line segment between A and B. Find the midpoint of that line segment, and then draw a plane perpendicular to the line segment, specifying that that plane also includes the midpoint of the line segment AB. Same thing. The set of all points that make up that plane will be equidistant from A and B. At the risk of running it into the ground, given a line segment AB, if the line segment is bisected by a plane perpendicular to the line segment, it (the plane) will contain the set of all points equidistant from A and B.
What else can I help you with?
What 3-dimensional figure is made from a set of points in space that are equidistant from a fixed point?
A sphere.
Which name desrcribes the set of points equidistant from a given point in space?
Sphere?
What solid bounded by the set of all points at a given distance from a given point?
The solid bounded by the set of all points at a given distance from a given point is a sphere. The center of the sphere is the given point, and the radius is the specified distance. All points on the surface of the sphere are equidistant from the center, forming a perfectly symmetrical shape in three-dimensional space.
What is a set of points in space equidistant from a given point called?
A set of points in space that are equidistant from a given point is called a sphere. The given point is referred to as the center of the sphere, and the distance from the center to any point on the surface is known as the radius. In three-dimensional space, a sphere is defined mathematically by the equation ( (x - h)^2 + (y - k)^2 + (z - l)^2 = r^2 ), where ((h, k, l)) are the coordinates of the center and (r) is the radius.
A set of point that is equidistant to a fixed point called center?
A set of points that are equidistant from a fixed point, known as the center, forms a geometric shape called a circle. In a two-dimensional plane, all points on the circle are the same distance from the center, which is defined as the radius. This concept can be extended to higher dimensions, where the set of points equidistant from a center forms a sphere in three-dimensional space.
What 3-dimensional figure is made from a set of points in space that are equidistant from a fixed point?
A sphere.
What 3-dimensional figures is made from a set of points in space that are equidistant from a fixed point?
Sphere
A example of how a sphere is similar to a circle?
A circle, rotated about any diameter, will generate a sphere with the same radius. A circle is the locus of all points in 2-dimensional space that are equidistant from a fixed point. A sphere is the locus of all points in 3-dimensional space that are equidistant from a fixed point.
Which name desrcribes the set of points equidistant from a given point in space?
Sphere?
What solid bounded by the set of all points at a given distance from a given point?
The solid bounded by the set of all points at a given distance from a given point is a sphere. The center of the sphere is the given point, and the radius is the specified distance. All points on the surface of the sphere are equidistant from the center, forming a perfectly symmetrical shape in three-dimensional space.
What is a set of points in space equidistant from a given point called?
A set of points in space that are equidistant from a given point is called a sphere. The given point is referred to as the center of the sphere, and the distance from the center to any point on the surface is known as the radius. In three-dimensional space, a sphere is defined mathematically by the equation ( (x - h)^2 + (y - k)^2 + (z - l)^2 = r^2 ), where ((h, k, l)) are the coordinates of the center and (r) is the radius.
A set of point that is equidistant to a fixed point called center?
A set of points that are equidistant from a fixed point, known as the center, forms a geometric shape called a circle. In a two-dimensional plane, all points on the circle are the same distance from the center, which is defined as the radius. This concept can be extended to higher dimensions, where the set of points equidistant from a center forms a sphere in three-dimensional space.
What would be a 3 dimensional version of a circle?
A three-dimensional version of a circle is a sphere. While a circle is a two-dimensional shape defined by all the points equidistant from a center point in a plane, a sphere extends this concept into three dimensions, comprising all points equidistant from a central point in space. Just as a circle has a radius, so does a sphere, which determines its size.
What is a space figure who set of all points on the surface are equidistant from the center?
A sphere would fit the given description.
What is a set of points in a plane that are all the same distance from a given point?
In 2-dimensional space, a circle. In 3-dimensional space, a sphere.
What is the locus of points in space that are equidistant from two parallel planes?
A plane midway between the two given planes and parallel to them.
The locus of all points in space equidistant from a given point?
That's a sphere whose radius is the constant equal distance.
