Can anybody help me on this problem please.

For any points ABCD are arranged along a line such that AC>AB and BD<BC. Draw a picture with the four points in plane. Is there more than one order possible?

Thanks a lot

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- December 17th 2010, 05:19 AMrcsany more possible arrangement of AC>AB and BD<BC
Can anybody help me on this problem please.

For any points ABCD are arranged along a line such that AC>AB and BD<BC. Draw a picture with the four points in plane. Is there more than one order possible?

Thanks a lot - December 17th 2010, 05:32 AMemakarov
Have you tried drawing a line with A, B, C such that AB < AC and then trying to insert D so that BD < BC? I know it's just a restatement of the problem, but I don't see any difficulty in this problem other than trying a few cases.

- December 17th 2010, 05:33 AMPlato
- December 17th 2010, 06:04 AMrcs
i think it is about the segment sir

- December 17th 2010, 06:26 AMPlato
If it is simply length of a line segment then will give .

Can you find another? - December 17th 2010, 06:33 AMrcs
DC<DA ... is that correct sir

- December 17th 2010, 06:43 AMPlato
- December 17th 2010, 06:58 AMrcs
DC is shorter than DA ... am i correct sir ?

- December 17th 2010, 06:59 AMSoroban
Hello, rcs!

Quote:

. .

Using emakarov's suggestion, I found 12.

The following six and their mirror-images.

Did I miss any?

- December 17th 2010, 07:04 AMrcs
oh my God! u mean their mirror images are the opposite arrangement sir soroban?

like A-B-D-C its mirror is C-D-B-A ? am i right sir?

thanks alot - December 17th 2010, 09:00 AMPlato
This is precisely why I asked for clarification as to exactly what is involved here. I assumed that this question has to do with ordering collinear points using some form of Hilbert’s

*betweenness axioms*. If that is correct then there is only one possible order: .

There is no notion of a mirror image in the axioms.

Short of something like Ed Moise’s*ruler axiom*spacing makes no difference.

To be clear on what this means, given we know that .

BUT there is no way to compare , without knowing the full context of the question. - December 17th 2010, 05:37 PMrcs
sir plato, what do mirror images meant for?

- December 18th 2010, 04:22 AMPlato