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Naming Coplanar Points?

Posted on 2012-08-29
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Last Modified: 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.
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Question by:naseeam
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by:naseeam
ID: 38345583
Sorry,  forgot to attache the figure.
coplanar-figure.jpg
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d-glitch earned 1200 total points
ID: 38345645
Every set of 3 points is coplanar.
This particular plane will cut the box in half along the CG face diagonal.
It will also go through point H by symmetry.
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Assisted Solution

by:d-glitch
d-glitch earned 1200 total points
ID: 38345673
Imagine the plane that contains ABCD, the top of the box.
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.
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Expert Comment

by:sdstuber
ID: 38345682
Can we assume the figure is symmetric?  If so, then I agree H should be coplanar with the other 3.

If the EH edge is shorter or longer than FG then no named point will be coplanar with BCG
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by:aburr
ID: 38345684
d-glitch has given you the essential information. As he said ANY three points can be used to define a plane. A possible solution for your problem is to find the equation for your plane.
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.
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Author Comment

by:naseeam
ID: 38345827
>>  This particular plane will cut the box in half along the CG face diagonal.

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?
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by:TommySzalapski
ID: 38345832
sdstuber, given that it's a high school geometry question, I'm sure we can assume that it's just a rectangular prism so d-glitch's answer is correct.
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by:sdstuber
ID: 38345948
I agree it's probably correct, but some of the rules of geometry drilled into me in high-school was that just because the drawing "looks" symmetric doesn't mean it is.  Just because an angle "looks" like a right angle doesn't mean it is.

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.
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by:naseeam
ID: 38345987
Are there other correct answers besides point H?

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?
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Assisted Solution

by:TommySzalapski
TommySzalapski earned 800 total points
ID: 38346010
No. You can't actually move things. d-glitch was just trying to give you a visual.

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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Assisted Solution

by:TommySzalapski
TommySzalapski earned 800 total points
ID: 38346018
Another way of looking at it. If you had the real 3D figure and took a sheet of paper and aligned with B, C, and G. Notice that it will also touch H. The paper represents the plane.
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Author Closing Comment

by:naseeam
ID: 38346122
Multiples solutions,  Multiple explanations.  Follow up great explanations.  Tremendous help.
They really explained from all angles.  It's impossible not to understand!

Thank you so much!
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