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Saumyojit

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There are 10 straight lines, no two of which are parallel and no three of which pass through any common point, are drawn on a plane. The total number of regions into which the plane would be divided by the lines is


Finite and infinite region how to comprehend the no of regions?
What will be the diagram?
 
Saumyojit said:
There are 10 straight lines, no two of which are parallel and no three of which pass through any common point, are drawn on a plane. The total number of regions into which the plane would be divided by the lines is


Finite and infinite region how to comprehend the no of regions?
What will be the diagram?
Click to expand...
What have you tried? What diagram have you drawn? Surely you know better than this.

A good approach is to start with a smaller problem -- in fact, with a sequence of smaller problems. This can help both in understanding what is being asked, and in seeing a pattern.

So, with 2 lines fitting the requirement, how many regions is the plane divided into? Then 3 lines, 4 lines, and so on?
 
two lines crossing.png

There is one infinite region and i am not able to calculate no of finite regions?
 
Saumyojit said:
There are 10 straight lines, no two of which are parallel and no three of which pass through any common point, are drawn on a plane. The total number of regions into which the plane would be divided by the lines is


Finite and infinite region how to comprehend the no of regions?
What will be the diagram?
Click to expand...
I'm confused again. The problem, if you quoted it accurately, doesn't distinguish finite and infinite regions, and I see no reason to distinguish them in solving the problem as stated.

Did you fail to follow the rules and state the problem exactly and completely?? If so, shame on you; if it's as stated, why do you think it matters?
Saumyojit said:
View attachment 28934

There is one infinite region and i am not able to calculate no of finite regions?
Click to expand...

pka is right: You seem to be thinking about finite segments, not [infinite] lines as the problem states. If you use segments, then you will always get exactly one infinite region! And the number of finite regions would depend on where the segments end.
 
Saumyojit said:
ok yes 4 infinite region but how many finite?
Click to expand...
Count them! Do you see any? No, there are 0 finite regions in the case of 2 lines. The total is 4.

The question doesn't require you to distinguish finite and infinite regions! It only mentions them (the part you failed to copy for us) in order to make it clear that they don't want you to count only finite regions. So don't make the problem harder than it is.

Now, continue. What happens with 3, 4, 5 lines? Look for a pattern.
 
one line 2 infinite
2 line 4 infinte
3 line 6 infinite and one finite
4 line 3 finite and eight infinite ..
5 line 6 finite , ten infinite
....
.
.....
10 lines 56 region all total


Why all the lines when drawn in a plane have to intersect each other exactly once? this is a question i discovered right now?
 
Last edited:
Saumyojit said:
Why all the lines when drawn in a plane have to intersect each other exactly once? this is a question i discovered right now?
Click to expand...
Why do you think that's true? Did you read it somewhere, or did you conclude it from something you tried?

Have you tried answering your own question? That is the way to learn to think.
 
2 lines.
When you draw a 3rd line how many more regions do you get?
When you draw a 4th line how many more regions do you get?
When you draw a 5th line how many more regions do you get?
When you draw a 6th line how many more regions do you get?
When you draw a 7th line how many more regions do you get?
....

Do you see any patterns? Patterns is what mathematics is all about.
 
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