Question

Determine whether the statement is true or false:
↔RV is in plane S.

Answer 1

No, because V is in the plane P and not in S.

Answer 2

Thank you. This is what I thought too, but what I don't understand is how is the question possible if point R is on one plane and point V is on another?
Because I have another question:
A line connecting Q and T intersects ↔MN.
but Q and T aren't on the same plane, so does that negate the question and make it false? Or is there a way to connect Q and T?

Answer 3

Of course there is a way to connect Q and T, you just have to make a segment between them. But, the segment is out S and out P. It's on another plane.

Answer 4

You can connect R and V too, but like connecting Q and T, it will be in another plane, don't mentioned.

Answer 5

In that question, A line connecting Q and T intersects ↔MN, it's false.
Because MN is on the intersection of S and P (so, MN is on S and on P), but QT are totally out of these plans, so, it wouldn't intersect.

Answer 6

It's hard to me to explain these things in English. I'm Brazilian and my English is not that good.

Answer 7

So, what you're saying is... if there are two points on two different planes, they CAN connect, but in doing so they would make their own plane?

Answer 8

Yes. That's it.

Answer 9

I can understand you, and appreciate it :) you have been very helpful!

Answer 10

But you can't define that plane created by these new segment, because a plane is defined by two lines.

Answer 11

I thought a plane was defined by four connecting lines?

Answer 12

If you say that a plane was defined by four connecting lines, you're saying that the plane is finite.

Answer 13

But the plane is infinite.

Answer 14

Are we talking about Euclidean Geometry?

Answer 15

Um I'm not sure about the Euclidean part but yes, Geometry.

Answer 16

Ok, the plane is defined by two parallel lines. I thinked and you're right, because if there are two paralel lines, there's 4 points that's you can connect in the same plane.

Answer 17

But i'm sure that you can't define a plane if only one segment kk

Answer 18

So, QT is defined, it's in a plane (every segment is in a plane), but you can't define that plane especifically.

Answer 19

and QT is out of S and P.

Answer 20

It's more easy to see it when you have the coordinates of the points to generate the equation and see it ;D

Answer 21

Yeah I think that's why I have a problem with Geometry because it is so spacial and I have a hard time visualizing it. I have another problem...will you help me with it?

Answer 22

Of course.

Answer 23

At what point(s) do plane JIF and plane FEH intersect?
-points I and F only
-line IF
-points I, F, H, and G only
My problem is, I only see one point that is the same on JIF and FEH ...that point is F

Answer 24

F and I and all the points that are between F and I. So the answers is line IF.

Answer 25

Remember that in a line there are infinite points? So, all these points are on the intersect, plus F and I.

Answer 26

The intersect means where they all touch? I thought because F was the only point both planes had in common, it was the right answer. Also because I is not in plane FEH, is it?

Answer 27

FEH is in the plane FEH, you can see that visualizing and if its in the name of the plane haha

Answer 28

See that image:

Answer 29

The planes are infinites. In pink are the FEH plane and green is the JIF plane.

Answer 30

The line IF it's the place where they cut each other. Like when you cut a bread, you choice a line and cut it, right? That's the same in the planes. They don't cross each other in a point, they cross each other in a line.

Answer 31

I think the problem is that you're thinking that the planes are touching, they're crossing out. They're infinite.

Answer 32

That makes so much sense!

Answer 33

Another example. The purple and the green one are planes. The red line are the place they cross each other.

Answer 34

Okay, so I'm starting to see it a little better. What about this one?
At what point(s) do plane JAB, plane ABC, and plane HEC intersect?
-AB
-points A, B, and H only
-point B only
-They do not intersect.
(It's the same picture I sent you)
I am trying to look at it as infinite and not just connecting points...is the answer B only?

Answer 35

Same picture?

Answer 36

Yes, same picture, here it is

Answer 37

Let's do it in parts: First of all, you have to see where the plane JAB and ABC intersects. Can you see it?

Answer 38

AB?

Answer 39

Yeah!

Answer 40

Now you have where HEC intersect AB.

Answer 41

Um... I kinda see HB as an intersection of JAB and HEC..?

Answer 42

Yes.

Answer 43

You got to another way, but it's correct to. If the intersects of JAB and HEC its HB and the intersect of JAB and ABC is AB, then the intersect of the three of them are the intersect of AB and HB.

Answer 44

It's B.

Answer 45

Hey so I got it right!

Answer 46

Yeah! look at the picture with the planes .

Answer 47

Ohhh abc is on the bottom. I was having a hard time with that one but it makes sense!
This one is difficult for me too..
(Same picture) A line connecting points B and G would lie in which plane
-ABC
-FGD
-JIH
-IFE

Answer 48

I am having a hard time visualizing DGF but the other two options don't seem correct.

Answer 49

What is 'lie'? Sorry for my english rs it's like cross?

Answer 50

I don't understand what the question says ;s

Answer 51

Ok I'll rephrase the question:
a line connecting B and G would be on which plane?

Answer 52

that's better ! :] so i will think about it...

Answer 53

I think it's none of these plans man, i think the plan is not defined. I will draw it better.

Answer 54

Are you sure it's B and G?

Answer 55

Okay. So do they create their own plane, then? And yes, B & G.

Answer 56

yes, they create another plan. look at that picture:

Answer 57

Don't look at the letters, they're changed, but , look at the segment. it is not in any plane.

Answer 58

From another point of view:

Answer 59

Thank you so much!
I think I might be getting it a little more now.
I have a problem visualizing GF. I can't figure out how that plane would look. (Same picture)

Answer 60

Would it be sideways?

Answer 61

GF don't define a plane, you need three points to define a plane. I can show you infinites planes that GF is inside.

Answer 62

Well my question asks where BC and GF would intersect... but do they not intersect because they are not planes?

Answer 63

BC and GF will never intersect. It's not because they're not planes, it's possible that two lines intersect each other, but, BC and GF are in different planes and planes that don't intersect so BC and GF can't intersect too.

Answer 64

Okay I can understand that.

Answer 65

Just imagine BC and GF prolongating, you will see that it will never intersect.

Answer 66

Okay that makes a lot of sense. What about three points where two are on the same plane, like J and H, and one that is not, like D...does that make anything?

Answer 67

It will define a new plane! That time defined, because you have three points. You can call this new plane JHD.

Answer 68

Okay :) So if the question asked if those three points were coplanar or non-coplanar, would the new plane apply? Or not because that plane wasn't in the example picture?

Answer 69

Three points are always coplanar.

Answer 70

Even if the plane wasn't in the picture?

Answer 71

Even if the plane wasn't in the picture.

Answer 72

You can say it for three points, but, for example: Are J, I, H and D coplanar? It's false.

Answer 73

Are J, H, I and A coplanar? It's true. You have to analyse. But when it's three points, always coplanar.

Answer 74

You have been SO helpful :) thank you!!

Answer 75

you welcome :]

Answer 76

I am new to this site. if I am your fan, does that mean I can find you again?

Answer 77

Yeah, that's it. I will be on your fan list (its the button in the right of the mini-letter of messages) and you will see if i'm online :]

Answer 78

thanks again :) expect me to ask you lots of questions later! I'm learning Geometry and you're better than my teacher haha

Answer 79

you welcome :] feel free to ask me more questions, when i try to explain something i'm studying too ;]

Answer 80

Your English is great! also, lie means 2 things: one is to say something that is not the truth...
but the way my question used it means "to be on". (Usually it is horizontal. "The person lies on the couch." "The book lies on the table." Both these things are laying down/horizontal.) Hope that I helped you back some :) bye for now!

Answer 81

bye :] good night.