Thread: any 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

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.

Originally Posted by rcs

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?

You need to explain the notation. What does stand for?
Is it simply the length of line segment ?
Or is it a signed length? If we arrange , B is between A & C, then using just length we have .

Do you see what we need to know about the notation?

i think it is about the segment sir

If it is simply length of a line segment then will give .
Can you find another?

DC<DA ... is that correct sir

Originally Posted by rcs

DC<DA ... is that correct sir

Why do you think that works?

DC is shorter than DA ... am i correct sir ?

Hello, rcs!

. .

Using emakarov's suggestion, I found 12.
The following six and their mirror-images.














Did I miss any?

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

Originally Posted by Soroban

[size=3]Using emakarov's suggestion, I found 12.
The following six and their mirror-images.

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.

sir plato, what do mirror images meant for?

Originally Posted by rcs

what do mirror images meant for?

@rcs
Unless you post the exact statement of this problem along with all definitions and relevant axioms, it is pointless to continue this thread.