ID:184537
 
Today in class me and my teacher argued about something and I was wondering if you guys could clarify.


The question was:



What point do PS and SR intersect at?

Now, the definition in the book says that it takes two lines for an intersection. He claimed that it intersected at S but I said no, because its only one line, just named differently.


Which is it?
it depends on the wording of the question. If it asks about the line segments, than the teacher would be correct.

Usually on questions with a continuing line, it asks about line segments.

§atans§pawn
If PS and SR are line segments, I suppose they intersect at S. If they're lines, then they intersect on an infinite number of points.
Infinitly many points.
In response to Jon88
But how is that two lines? I thought for an intersection to even happen, you need two lines. It's one line, just named differently. That's where I got confused about it. The definition of Postulate 4 was that if two lines intersect, they interesect at a point. It's only one line. :-(
In response to XxDohxX
XxDohxX wrote:
It's only one line. :-(

It's only one line, but it makes three line segments.
Also, there is no rule that lines cannot overlap and still be compared.

I agree with them. It's either at point S, or infinately along the line.
In response to DarkCampainger
Well, to clarify, it was talking about the whole line itself, and naming the line--line PS and line SR.
I forgot to include that.

Anyways, but the definition said it needed TWO lines. I don't see how one line can be two.

Explain to me how ONE line ends up being TWO. :-(
In response to XxDohxX
Well, you're thinking it in terms of the drawing. Forget about that. You have line PS and line SR. Without drawing a diagram or receiving any extra information, you should be able to assume the line PS intersect line SR at S, and vice versa.

Also, it's not one line becoming two. It's two lines becoming one. PS and SR form the line PR. Infact, now that I think about it, PS and SR are looking more like rays to me.
In response to DarkCampainger
Well, they DID give me a diagram, maybe thats where it confused me.
In response to DarkCampainger
DarkCampainger wrote:
XxDohxX wrote:
It's only one line. :-(

It's only one line, but it makes three line segments.
Also, there is no rule that lines cannot overlap and still be compared.

I agree with them. It's either at point S, or infinately along the line.

It is only one line, yes. However, it forms a minimum of 4 segments. PS, SR, and either direction from them leading outwards. >_>

Just felt the need to point that out.

§atans§pawn
In response to XxDohxX
XxDohxX wrote:
Well, to clarify, it was talking about the whole line itself, and naming the line--line PS and line SR.
I forgot to include that.

Anyways, but the definition said it needed TWO lines. I don't see how one line can be two.

Explain to me how ONE line ends up being TWO. :-(

This all leads back into my first reply, where they are segments of a line. I am pretty sure I can make a fairly close guess at what the question actually reads...

"What point do line segment PS and line segment RS intersect at?"

or something close to those lines.

If you want, you can say that everything from the two points make up a line, thus leaving you with two lines that intersect at the middle dot.

§atans§pawn
In response to Satans Spawn
Satans Spawn wrote:
It is only one line, yes. However, it forms a minimum of 4 segments. PS, SR, and either direction from them leading outwards. >_>

Line segments don't have direction. You must be thinking of rays or vectors.
In response to DarkCampainger
DarkCampainger wrote:
Satans Spawn wrote:
It is only one line, yes. However, it forms a minimum of 4 segments. PS, SR, and either direction from them leading outwards. >_>

Line segments don't have direction. You must be thinking of rays or vectors.

I simply mean that the line the segments are a part of continues in both directions which will create two more segemtns which will never end... I might be wrong because its been a few years since I have been in a math class, but math was always my best subject when I applied myself, and I enjoyed Geometry...

§atans§pawn
In response to Satans Spawn
http://mathworld.wolfram.com/LineSegment.html
"A closed interval corresponding to a finite portion of an infinite line"

Nope, I'm pretty sure you're thinking about rays for the "continues" part.
In response to DarkCampainger
I see... either way, I was corrected, and con now correctly correct whomever I was originally correcting...


There are only 2 line segments >_>

§atans§pawn
XxDohxX wrote:
Now, the definition in the book says that it takes two lines for an intersection. He claimed that it intersected at S but I said no, because its only one line, just named differently.

The books are never 100% right. I once had a math book that said an angle is formed by 2 rays, and only rays. When my teacher asked how many angles were in the hexagon, I said 0, because the hexagon was made up of line segments, and not rays.

Got in trouble for that :[
There's nothing that says that two lines cannot occupy the same space, and share the same points...

A line is defined by an equation, and if two equations are equivalent, the lines they define will overlap... However, they're still two distinct lines (well, until you simplify one or the other equation into being the exact same equation)

Also, a line is an infinite number of points, correct? So there's plenty to go around...lol You can't say that one line occupies all of the available points, because with infinite points, there's no point at which you "run out"... Another line can simply sit right on top of each and every point of the other line, using the points that are "in between" the ones that the other line is using (of course, since we're dealing with infinity here, there is no "in between", and both lines are simultaneously using all of the points, but it's easier to visualize it this way)

In our minds (and on paper) it's pretty much impossible to think of it this way... Our rules of reality clearly tell us that no object can occupy the same space as another... But the trick is that lines (and points) occupy no space at all... You can stack an infinite number of them right on top of each other...

However, by this statement, those two lines intersect at all points, not just one like it seems to be asking for...

So, it leads me to believe that they intended it to say "line segments"... Or, even that it did call them line segments (your post doesn't specify, it just gives the letters)...

In this case, they intersect at their only common point, S ("intersect" doesn't mean "cross"... it simply means "they share a point", even if that point is on the end)

In the problem, were there lines drawn above the PS and SR? If so, did those lines have arrows on the ends of them? If they did, then it is to be read as "line"... If they did not, then it is "line segment"...

[Edit:] I've got to clarify that last statement... They are defined as "lines" if the little line symbol drawn above them has an arrow on both ends... If there is only an arrow on one end, then it is a "ray" (and again, with no arrows, then it is "line segment")

http://everydaymath.uchicago.edu/samplelessons/3rd/ srb04.html
The english definition of intersection isn't limited to lines. Rays and segments, pop cans and people can intersect.
In response to XxDohxX
I bet the postulate was being general. What else would you call them if you wanted to include everything?
In response to Satans Spawn
If they share a point, they intersect.
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