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How many lines are determined by 12 points no 3 of which are collinear?
Wiki User
∙ 8y ago
There are 66 lines.
As no 3 points are co-linear, every line passes through exactly two of the points.
Thus every point is joined by one of the lines to every other point.
So it looks like there are 12 × 11 = 132 lines.
However, the line joining point A to point B is the same as the line joining point B to point A; in other words, every line has been counted twice, once for one of the points it passes through and again by the other point it passes through.
Therefore there are half the number of lines discovered above, name 132 ÷ 2 = 66 lines.
This is the same as the "handshake problem" where everyone at a party shakes hands with everyone else at the party and the question is how many handshakes are there; the points are the people and the lines are the handshakes.
Wiki User
∙ 8y ago
Wiki User
∙ 8y agoSince you can combine any point with any other point, the answer is 12 over 2, which is the same as (12 x 11) / (1 x 2).
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Points a b c and d are coplanar b c and d are collinear not a how many lines are determined by a b c and d?
5 its 4
How many plane are determined by four non collinear points?
exactly nine planes! * * * * * I would have said 4 - corresponding to the four faces of a tetrahedron. Of course, non-collinear does not mean non-coplanar so all four points could be in the same single plane!
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.
How many different lines are determined by two points?
In classical or Euclidean plane geometry two points defines exactly one line. On a sphere two points can define infinitely many lines only one of which will represent the shortest distance between the points. On other curved surfaces, or in non-Euclidean geometries, the number of lines determined by two points can vary. Even in the Euclidean plane, two points determine infinitely many lines that are not straight!
How many non-collinear points are there in one plane?
There are an infinite number of any kind of points in any plane. But once you have three ( 3 ) non-collinear points, you know exactly which plane they're in, because there's no other plane that contains the same three non-collinear points.
If points S O and N are collinear how many lines do they determined?
3
How many different lines are determined by three non-collinear points?
3
How many lines are determined by 13 points no 3 of which are collinear?
There are 13*12/2 = 78 lines.
Points A B and C are collinear How many lines are determined by A B and C?
# 1
How many different lines are determined by 3 non collinear points?
Any three non-collinear points will define a single plane. A plane is composed of an infinite number of distinct lines.
How many different lines are determined by three collinear points?
As long as at least two of them are different points, exactly one line.
How many lines with 8 collinear points?
7.
How many straight lines can be formed with 3 collinear points?
only 1 lines can contain 3 collinear points. Maybe you mean coplanar?
How many planes are determined by 5 points three are not collinear?
10!
How many lines can be drawn out of 14 points on a plane with no 3 or more points collinear?
There are 91 lines.
Points a b c and d are coplanar b c and d are collinear not a how many lines are determined by a b c and d?
5 its 4
How many line can contain 3 non collinear points?
Two intersecting lines can always cover three non-collinear points.
