Question

How many different segments are determined by 6 points on a line?

Answer 1

Wanna see how to solve this?

Answer 2

Yes please.

Answer 3

I'm sorry, my internet died as I was trying to help. Are you still available?

Answer 4

lol yea

Answer 5

Ah... good.

Ok, so we literally just draw it out:

-------------------------------------------- we have a line here, ya?

Answer 6

Oh wait! Forgot something important. That's not a real line, because I forgot to do something important. Wanna tell me what I forgot to do?

Answer 7

Hint: It's a line in non-math terms, but mathematical lines have a big difference between "real world lines" and "mathematical lines".

Answer 8

uhm points?

Answer 9

Well, an unlimited amount of points, right? So I should have drawn:

<----------------->

Answer 10

(I'll show you why it's important later)

Answer 11

Let's make believe a * is a point.

So, let's drop six random points.

<----*----*--*----*----*---*----->

Ok, so this might be a little tricky. Tell me first what a line segment is.

Answer 12

A line linking two points?

Answer 13

Kinda. A line cut by two points. The problem is that when we say "line" in the math world, we have to make sure we don't mix it up with a line in real life.

I can draw a line on a piece of paper if I'm using 'real life lines'. But mathematically, I can only draw a line segment on a piece of paper. Sorry if that seems super geeky, but it's important to say the difference. But yeah. You're right. :D

Ok, so a quick test: Is this a line segment? *---->

Answer 14

It is.

Answer 15

It's not. :(
While it starts at a point, it goes on forever to the right. A line segment can be measured. But the arrow means that it goes on forever, so you can't ever measure it.

Does that make sense?

Answer 16

(That's called a ray, by the way)

Answer 17

Oohh oops lol i think i get the difference now.

Answer 18

Perfect! So you tell me:
<----*----*--*----*----*---*----->

How many segments are there with six points?

Answer 19

7 segments.

Answer 20

Careful! Remember the rays.

Answer 21

*--> goes on forever, so it's a ray, not a segment.

Answer 22

Oh right so no segments?

Answer 23

<-* is also a ray that goes on forever to the left. Easy way to remember it: a line segment is a line segment ONLY if there's a point (a * in our picture) on both the right and the left.

Answer 24

Well, look at it again. Are there any measureable points on this thingy: <----*----*--*----*----*---*----->

Answer 25

5 segments?

Answer 26

Imagine it this way: the entire line is an infinitely large roll of ribbon. The points are where you cut the ribbon. So if we snipped at the ribbon (the line) at those six points, how many measurable pieces of ribbon do we have?

Answer 27

Exactly! Five segments. :D

Answer 28

Now, I just want to double check that you understand this.

If I have a ray that keeps going to the right forever, and I put 3 points on it, how many segments do I get? Imagine that the first point is the original point on the very left side.

Go ahead and 'draw' me a picture with dashes and an arrow and a * to show me how you solve it.

Answer 29

*__*__*__> is that correct?

Answer 30

Yes! So how many segments?

Answer 31

2

Answer 32

Beautiful! You've mastered this stuff. Have fun acing the test!

Answer 33

Lol thank you for explaining that to me. But given that it is not a ray how many different line segments will there be?

Answer 34

Well, that depends. Was the original thing a line segment or a line?

Answer 35

The answer choices are 12, 15 ,17, 21 or 30.

Answer 36

Hmm.... how many times did it say that you have to cut it?

Answer 37

I mean... how many points did it want you to put? And was the original thing a line or a line segment?

Answer 38

6 points. The question is my original question exactly.

Answer 39

Oh!!! It's kind of a trick question. I see now.

<--A---B---C----D---E---F--->

Answer 40

each letter is a point. They're being sneaky and want us to count stuff like "segment AC".

Answer 41

mhm

Answer 42

So, let's see...

AB
AC
AD
AE
AF

BC
BD
BE
BF

CD
CE
CF

DE
DF

EF

Answer 43

Does it make sense why it got shorter each time I went to a new letter?

Answer 44

Because they are separate line segments?

Answer 45

So 15 different segments?

Answer 46

They are, but I mean do you notice how when I made the list, I started with AB, then made it one step bigger, then one step bigger, etc?

Then, when I got to B, because we already did segment AB, I didn't write BA. That's why each group got shorter by 1 each time.

Answer 47

That's right. I got 15.

Answer 48

Right tysm for explaining! :)

Answer 49

No prob. Good luck on the test.