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What is a set of points in a plane that are a given distance from a given point in a plane?
a circle
What is a set of points in a plane that are the same distance from a given point in the plane?
They are points on the circumference of a unique circle in the plane.
Do planes contain exactly three points?
No. The tiniest piece of a plane contains an infinite number of points. But if you give us just three points, then we know exactly what plane you're talking about, and it can't be any other plane.
Through any three points there exists exactly one plane?
Collinear points
Does a plane containing two points of a line contains the entire line?
yes
In general how many planes are there which contain any number of given points?
There are no planes containing any number of given points. Two points not the same define a line. Three points not in a line define a plane. For four or more points to lie in the same plane, three can be arbitrary but not on the same line, but the fourth (and so on) points must lie in that same plane.
What is the greatest number of planes that can pass through three collinear points?
The points are collinear, and there is an infinite number of planes that contain a given line. A plane containing the line can be rotated about the line by any number of degrees to form an unlimited number of other planes.If, on the other hand, the points are not collinear, then the plane has no wriggle room: it is stuck fast in one place - there can be only one plane containing all the points. Provided they are non-colinear, three points will define a plane.
What is a set of points in a plane that are a given distance from a given point in a plane?
a circle
Can 3 points be non-coplanar is outside the plane?
If you are given a plane, you can always find and number of points that are not in that plane but, given anythree points there is always at least one plane that goes through all three.
What is a set of points in a plane that are the same distance from a given point in the plane?
They are points on the circumference of a unique circle in the plane.
Do planes contain exactly three points?
No. The tiniest piece of a plane contains an infinite number of points. But if you give us just three points, then we know exactly what plane you're talking about, and it can't be any other plane.
Is a line joining two points not necessarily in the plane containing the two points?
If it is a straight line it must be in the same plane. Otherwise not necessarily.
Through any three points there exists exactly one plane?
Collinear points
Does a plane containing two points of a line contains the entire line?
yes
Through any three points there is exactly one plane cointaining them?
I think you mean: Are any three points contained in exactly one plane? only if they're not collinear... I think
Which geometric object is defined as the set if all points in a plane at a given distance at a given point?
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.
Are three points always contained in exactly one plane?
Three points determine exactly one plane.That means that if you bring me a plane, then some or all of my three points may ormay not lie in your plane. But if you bring me three points, then I can always draw aplane in which all of your points lie, and I can also guarantee that it's the only one.By the way ... three points also determine exactly one circle.
