If four points are coplanar, then they are also collinear ?

Question

If four points are coplanar, then they are also collinear?

True or False

Answer 1

FALSE.. they could be in a common plane (imagine 4 points as in a rhombus , but they don't form a single line.

The other answer below me is incorrect... three points can be arranged like a triangle and they too would not be colinear.

Answer 2

They may or may not be collinear. If these 4 coplanar pointsall lie on the same line that lies on the plane, then they are collinear. But it is also possible that these 4 coplanar points are not contained on the same line, thus, they are not collinear. Hence, we say coplanar points are NOT ALWAYS collinear

Answer 3

It is false

Collinear means on a straight line and coplanar means they are in one plane

Coplanar may not be collinear but collinear may be coplanar

Answer 4

False many times. but it is true in special cases only.

If four points are co-planar means that all the four points lie in a single PLANE. But where as when 4 points are co-linear then all the points lie on the same LINE.

There is a difference between line and plane. Plane has many lines in it. In the same way that a planet in solar system.

So when four points are in a plane it doesn't mean that all of those should lie on same lie on a single line. So If four points are coplanar, then they are not collinear always.

But there is a possibility that you can choose 4 points that are in a plane(co-planar) which lie on the same line(co-linear).

Hope you can understand this explaination.

Answer 5

Collinear Points: Collinear Points are points that are all in one line.

AND

Coplanar Points: Coplanar points are points all in the same plane.

T - IF they meet the conditions above.



F- You could have a colinear line on 4 seperate planes..... OR You could have points in the same plane but the points are not in a line..

Answer 6

Not necessarily. Think of it this way, the verticies of a square are coplanar (since the square is drawn on a plane-the paper), but the vertices are not collinear (there is no one line that contains the four points).

Answer 7

no - the four points of a square are coplanar, but they clearly do not lie on the same line and are therefore NOT collinear

Answer 8

Uh... coplanar means on the same plane. Collinear leans on the same line. You can arrange four dots so they would be on the same plane, but not in the same line.

So the answer is... Not Necessarily. Is it possible? Yes. Is it true for all cases? no.

It would be with three dots, though.

Answer 9

could be true or false... coplaner does not make it true or false.... they could all lie on a circle... and they would be coplaner but not collinear.

Answer 10

false. take the case of a quadilateral or a rectangle.