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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?
Wiki User
∙ 15y ago
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.
Wiki User
∙ 15y ago
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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 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.
What is a two dimensional space formed by an infinite set of points?
There is no such thing as a two-dimensional space. By virtue of being a space, you are talking three dimensions. It sounds like what you're really asking is: What is a two-dimensional AREA bounded by an infinite set of points (or infinite number of sides - same thing)? Typically, that would be a circle...however you didn't specify the points all had to be equidistant from its center so it could be any irregular shape containing at least one curve (any curved portion would automatically have to contain infinite points). The best way to ask the question so that the only answer would be 'a circle' is: What is a two-dimensional area formed by an infinite set of points, all of which are equidistant from its center?
What 3-dimensional figures is made from a set of points in space that are equidistant from a fixed point?
Sphere
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?
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.
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.
The locus of all points in space equidistant from a given point?
That's a sphere whose radius is the constant equal distance.
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.
What is a two dimensional space formed by an infinite set of points?
There is no such thing as a two-dimensional space. By virtue of being a space, you are talking three dimensions. It sounds like what you're really asking is: What is a two-dimensional AREA bounded by an infinite set of points (or infinite number of sides - same thing)? Typically, that would be a circle...however you didn't specify the points all had to be equidistant from its center so it could be any irregular shape containing at least one curve (any curved portion would automatically have to contain infinite points). The best way to ask the question so that the only answer would be 'a circle' is: What is a two-dimensional area formed by an infinite set of points, all of which are equidistant from its center?
The set of points in space that are given the distance from a given point is?
surface area of a cylinder? No. In 2-dimensional space, a circle and in 3-d, a sphere.
Where do all the points in space equidistant from a given point lie?
I'm not sure, but I would imagine they would be 360O around the point and only in the same plane.
How do you place four points equidistant from each other?
you cannot do this on the plane. try proving this yourself. but a regular tetrahedron in space for example is an example where there four points equidistant from each other.
