Why/How are there infinite points in a line segment? A line may have infinite points becauase it may be expanded.But in case of a line segment it has 2 distinct points which are not movable.The distance between the end points in finite and known.
But still why do people(in my school) say that there are infinite points in a line segment.When I ask the teacher,she says you will learn at higher levels(what a genius way to get rid of question).
 A: Let's assume that your end points are A(0,0) and B(1,0).
Try to find a point in between them. Ok you found C(0.4,0).
Now try finding another point. Will you ever NOT be able to find another point? No, because there are infinite numbers between 0 and 1 (just think of decimals).
In the same way there are infinite points in a line segment.
A: Any segment with at least two points has infinitely many points, because, intuitively, given any two distinct points, there is a third one, distinct from both of them, say, the middle point.
If there were a finite number of points, there will be no point between say point 6 and point 7 (etc)
A: The concept of infinity is used for many different things, and one should not confuse them. A line, be it closed, open, straight, curved, finite in length, or infinite in length always consists of infinitely many individual points (at least for any reasonable notion of 'line'). This can be proven rigorously, and it's not hard at all. Basically, between any two distinct points on a line there is a third point between these two points (between should not necessarily mean the mid-point on a straight path connecting the points, and this may get a bit tricky, but not too tricky). The length of the line is a different issue. It may be finite in length or infinite in length. The totality of the points comprising the line is in any case infinite. In fact it can be shown (quite easily) that the cardinality of points of any line is always the same, so in a sense all lines have the same "amount" of points in them, though the way these points are arranged may give totally different geometric qualities to the line. 
A: The idea that line segments have an “infinite number of dimensionless points” is very common.
But it contradicts itself.
Badly.
(As you immediately recognized!)
Line segments must be made up of a finite number of points, where each point has an extension in space.
To argue otherwise (as is commonly done) is to contradict yourself.

If your points take up space (no matter how small).
And if you have an infinite amount of them.
Then you will have an infinite line.
(An infinite amount of anything is infinite.)
If your points take up NO space.
And if you have an infinite number of them.
Then you will have nothing at all.
(An infinite amount of nothing, is still nothing.)
Therefore, line segments must be made up of a finite number of points, where each point has an extension in space.
Each point must have an extension in space, because otherwise we get nothing (as we saw above.)
And there must be a finite number of points.
Why?
Because an infinite number of points (that extend in space), gives an infinite line (rather than a finite line segment).

Of course, the next question is: how many points are there in a given line segment?
This gets into the area of infinitesimals, and their inverses (unlimited numbers).
You can read more about the "rigorous" use of infinitesimals by googling "non-standard analysis" and "internal set theory".
Useful introductions can be found at these locations:

*

*Elementary Calculus: An Infinitesimal Approach https://people.math.wisc.edu/~keisler/calc.html (non-standard analysis)

*Internal Set Theory https://web.math.princeton.edu/~nelson/books/1.pdf, (other works here: https://web.math.princeton.edu/~nelson/books.html)

See pg. 25 of this chapter of Keisler in particular for an excellent visual depiction of these "infinitely" small/large numbers being viewed using an "infinity" microscope (for infinitesimals) and "infinity" telescope (for unlimited numbers): https://people.math.wisc.edu/~keisler/chapter_1b.pdf.

I prefer the Internal Set Theory approach of considering these numbers NOT as infinite per se, but "smaller/bigger than any real number you can think of, but not zero or infinite".
So, we propose a point, , on a line, to have a width of one iota, ι, where an iota is an infinitesimal number.
And how many iotas are there in a line segment of one unit?
A HUMONGOUS number, ,  of them! :)
Where  = 1/ι.
 is NOT infinite in size, just larger than any real number we can conceive of.
Now, a line segment of 2 units, would have twice as many points, its length given as (2×)×ι, and so on…

Sorry for the late, late reply.
You asked an excellent question, but were dismissed by your teacher with a non-response.
You can read more on this topic here: https://reduct.blog/articles/infinite-angels-dancing-on-a-pinpoint/
(I haven't written anything on the use of infinitesimals on my blog yet, but intend to over the next few months—they have some incredible uses)
