It is a surface with zero curvature. It is 2-dimensional and in those two dimensions it extends infinitely far.
It is a surface with zero curvature. It is 2-dimensional and in those two dimensions it extends infinitely far.
It is a surface with zero curvature. It is 2-dimensional and in those two dimensions it extends infinitely far.
It is a surface with zero curvature. It is 2-dimensional and in those two dimensions it extends infinitely far.
The set of all the points is the plane itself.
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line
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.
plane
The set of all the points is the plane itself.
The set of all points in the plane equidistant from one point in the plane is named a parabola.
A circle is the set of all points, on a plane, that is at a specific distance from a specified point (the center).A circle is the set of all points, on a plane, that is at a specific distance from a specified point (the center).A circle is the set of all points, on a plane, that is at a specific distance from a specified point (the center).A circle is the set of all points, on a plane, that is at a specific distance from a specified point (the center).
That set of points forms what is known as a "circle".
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line
A circle is the set of all points in a plane at a given distance FROM a given point, which is known as the circle's center.
They are all of the infinite number of points whose x-coordinate is zero.
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.
Circle
circle
circleA circle