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What is the vocabulary for belonging to the same line?
The term you are looking for is "collinear." In geometry, points that lie on the same straight line are said to be collinear. This concept is fundamental in understanding the properties of lines and angles in various geometric shapes. Identifying collinear points is crucial in solving problems related to coordinate geometry and spatial relationships.
How many lines contain n points with no 3 points collinear?
None. In ordinary geometry, a line contains an infinite number of points and, by definition, they are all collinear. In projective geometry, however, you can have three lines in the form of a triangle. Each line has only two points on it, so it cannot have 3 points collinear.
What does it mean for two points to be collinear?
"Collinear" means "on the same straight line".Two points are always collinear, because you can always draw a straight linebetween any two points. Three points may or may not be collinear.
How many different planes can pass through 3 non-collinear points?
In Euclidean geometry, only one.
Can three coplanar lines intersect twice?
In Euclidean planar geometry, not unless they're collinear, in which case they intersect an infinite number of times. In other types of geometry ... maybe.
