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How many planes contain the same three collinear points?
Infinitely many planes may contain the same three collinear points if the planes all intersect at the same line.
Can a plane contain one point of a line?
Yes, it can. A plane can contain any number of points of a line.
Does a plane contain at least three lines?
Yes- planes contain infinitely many points and every pair of points in plane determine a line in that plane, so every plane contains infinitely many lines.
Can a circle pass through three points of a straight line?
No, a circle can never pass through three points of a straight line. The circle will touch 1) no points of the line, 2) one point of the line (which is now tangent to the circle), or 3) two points of the line. A line can contain (at most) twopoints that lie on the line.
Can line segments have holes or missing pieces?
No it cannot because a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. If it has holes it does not contain every point between the end points.
How many planes can contain two given points?
If 2 points determine a line, then a line contains infinitely many planes.
How many points may a line contain?
A line, ray, or line segment contains an infinite number of points.
How many ordered pairs does any linear graph contain?
Equivalently, how many points does any linear graph contain? Equivalently, how many points does any line contain? Infinity.
How many planes contain the same three collinear points?
Infinitely many planes may contain the same three collinear points if the planes all intersect at the same line.
A line can contain an infinite number of?
points
Can a plane contain one point of a line?
Yes, it can. A plane can contain any number of points of a line.
How many line can contain 3 non collinear points?
Two intersecting lines can always cover three non-collinear points.
Can one line contain two points?
yes
Does a plane contain at least three lines?
Yes- planes contain infinitely many points and every pair of points in plane determine a line in that plane, so every plane contains infinitely many lines.
How many lines can contain a line and a point not on the line?
In plane geometry a line is a two dimentional object between two points. If a line or a point is not on the line it, by definition, does not contain them. The answer therefor is infinite. Unless it is a closed line which has a slightly different definition but the answer is the same.
Exactly one line may contain two points?
Yes and they are the end points
Does a line contain four non-coplanar points?
No, a line cannot contain four non-coplanar points. By definition, coplanar points are points that lie in the same plane, and any three points determine a plane. Since a line consists of an infinite number of points that are linear, any additional point beyond two points on a line will not be able to create a non-coplanar arrangement with those already on the line. Thus, four points on a line must be coplanar.
