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How many lines can be drawn through 5 non collinear points?
Through any two distinct points, exactly one line can be drawn. For 5 non-collinear points, each pair of points can form a line. The number of ways to choose 2 points from 5 is given by the combination formula ( \binom{5}{2} ), which equals 10. Therefore, 10 lines can be drawn through 5 non-collinear points.
What is noncollinear?
Non collinear refers to three or more points that are not all on the same straight line.
Can noncollinear points lie on a circle?
Yes. In fact, given any three non-collinear points, there is one (and only one) circle that passes through all three points.
Points on the same line are what?
Points on the same line can be many different things. In Geometry, they are said to be collinear. Though, usually the given information is linked with another question and a diagram, which would require a different answer.
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.
How many of non collinear points in plane?
Infinitely many. There are infinitely many points in the plane and although any pair of points define a line, no matter how many lines you are given, it is always possible to find a point that is not on any of them - that is, a point that is not collinear.
How do you find the number of rays given the number of point?
The answer depends on whether any of the points are collinear: that is, whether they lie on the same line. No matter how many points you have, if they are all collinear you will have only one ray.If you have N points, the maximum number of rays is attained when no three of them are collinear. This number is N*(N-1)/2.
How many planes will contain 2 points?
Infinitely many planes contain any two given points- it takes three (non-collinear) points to determine a plane.
Is it true if points are collinear they are also coplanar?
Yes, any points that are located on the same line will also be on the same plane. You can have more than one plane intersect a given line, but any points on that line will necessarily be on all the planes that intersect that line.
How many circles can pass through two given points?
Two points determine a unique line. Therefore, there are infinitely many circles that can pass through two given points. This is because a circle can be defined by its center, which can lie anywhere along the perpendicular bisector of the line segment connecting the two points.
What is the slope of the line that passes through the given points?
The slope of a line that passes through two points is (difference in y) / (difference in x).
How many planes can pass through two given points?
There are an infinite number of planes that pass through a pair of points. Select any plane that passes through both the points and then rotate it along the line joining the two points.
