Geometry Help Name an Example that shows that three points are always coplanar, but four points are not alway?

Question

Name an Example that shows that three points are always coplanar, but four points are not always coplanor

NEED HELP!!!

Answer 1

3 points are always coplanar---that is a postulate! Common sense.Example: draw 2 points on your floor and put a third point on the ceiling, is it possible to get a plane or flat surface like a sheet of drywall to pass through all 3 points? Yes!

  

4 points are not -- for example : draw 3 dots on your floor and 1 on the ceiling. There is no plane that will contain all 4 points.

Answer 2

Think of plane like a flat piece of paper that extends forever.

If you think about it, you could put a piece of paper (a plane) through any three points, no matter how the points are in space.

Now, to show that four points are not always in a plane.  Think of a piece of paper (representing a plane) that lies flat on a table with three points in it.  Then, think of a fourth point hovering above the table and above the paper (the plane).  As you can see, you can put a piece of paper (or a plane) through all four points at the same time.

I hope this helps you!  Please email anytime for further questions.

Answer 3

A triangle is a plane figure so that disposes off the first.

Now consider a tetrahedron. It has 4 faces all triangles Just stretch your forefinger, middle finger and thumb and rest their tips on the top of a table. that's the shape. These are 4 points which are not in a plane.

If your "mathematical" eyes are open, you will find that cameras are mounted on tripod for the same reason. No matter how thr ground is, tripod is always stable because it has 3 points of contacts with the ground which will be coplaner. If the camera were mounted on a chair, then there will be 4 points of contact with ground which may not be coplaner and the chair sometimes shakes of all the points are not in the same plane.

Answer 4

Think of it this way.

The ceiling in your bedroom (or whatever room youre in) represents a plane. Now imagine putting three dots anywhere on your ceiling. These three points are always coplanar.

Now think of those same three points. They are coplanar. Now, think of the very tip-top point on the roof of your house where all the sides of the roof, which represent planes, come together. The tip top point on your roof is not coplanar with the three points on your ceiling. Therefore, four points are not always coplanar

Hope I helped! Im pretty good at geometry, so email me anytime at [e-mail] if you ever need any help. Dont hesitate to ask!