coplanar-figure.jpg

Solved

Posted on 2012-08-29

Question is: Name a point that is coplanar with points B, C, and G.

I don't think B and G are coplanar because they are in different planes. It doesn't make sense to find fourth point that is coplanar with three given points. It looks like three given points themselves are not coplanar.

Please help in solving this problem. Explain the answer.

This is high school geometry problem.

The figure needed to solve this problem is attached.

I don't think B and G are coplanar because they are in different planes. It doesn't make sense to find fourth point that is coplanar with three given points. It looks like three given points themselves are not coplanar.

Please help in solving this problem. Explain the answer.

This is high school geometry problem.

The figure needed to solve this problem is attached.

12 Comments

Sorry, forgot to attache the figure.

coplanar-figure.jpg

coplanar-figure.jpg

This particular plane will cut the box in half along the CG face diagonal.

It will also go through point H by symmetry.

You can rotate this plane around the BC axis until it hits G. This is the plane you want.

It will contain the BC segment by definition, and the GH segment by symmetry.

If the EH edge is shorter or longer than FG then no named point will be coplanar with BCG

If you want your can rotate your coordinate system to set the plane in the xy plane. Then any two mumbers would represent a point on your plane.

This half box is not a plane until it is physically straightened so it becomes flat. Am I correct?

>> Imagine the plane that contains ABCD, the top of the box. You can rotate this plane around the BC axis until it hits G.

So, this will give same result as your other example. Correct?

The question and answer could be just as valid and high-school level to say "unknown" because answering "H" means relying on the "look" to declare symmetry.

What if we take the right side (plane DCGF) and lift it up 90 degrees, now we have plane

ABCDGF.

Now, points A, D, and F are coplanar with points B, C, and G. Am I correct or incorrect?

Try it this way:

Draw lines CH and BG. See how they form an X in the "diagonal plane" of the box?

The fact that something is coplanar doesn't mean the plane has been drawn, just that it could be drawn (i.e. it exists).

So the plane that connects those four points isn't currently drawn in the figure, but you could draw it. Thus, they are coplanar. Don't move any points.

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