# Thread: Quick Math Problem (No calculations needed): How many different planes are formed?

1. ## Quick Math Problem (No calculations needed): How many different planes are formed?

I just have a quick geometry question: Points A and B lie on line j, Points C and D lie on line k, and lines j and k intersect at some point (no name is given).
How many different planes are formed? It's a multiple choice...

A) exactly one
B) exactly two
C) infinitely many

Can you please provide a brief explanation? Thanks!

2. Originally Posted by I am bad at quick maths
I just have a quick geometry question: Points A and B lie on line j, Points C and D lie on line k, and lines j and k intersect at some point (no name is given).
How many different planes are formed? It's a multiple choice...

A) exactly one
B) exactly two
C) infinitely many

Can you please provide a brief explanation? Thanks!
What thoughts have you had on this problem so far? Do you know what a plane is?

Try to visualize it or draw it. Two lines intersect. Can every point in both lines be found to lie in a single plane, or are some of the points on those lines in a different plane?

Hint: how many planes did you need to make a drawing?

3. I get the answer to this question, but I have no idea how to slove it mathematically...

4. Originally Posted by Quick
I get the answer to this question, but I have no idea how to slove it mathematically...
Tell us what your answer is, and what your thoughts were that led you to it. It's entirely possible that what you thought was a perfectly good "mathematical" solution -- mathematics is not always a matter of special knowledge and magical formulas!

But there may be a postulate or theorem you would have learned; did you have reference to such a thing as part of your thinking?

On the other hand, did you quote the problem exactly? I wouldn't expect a math question to say just "How many different planes are formed?", without saying by what!

5. Originally Posted by Dr.Peterson
Tell us what your answer is, and what your thoughts were that led you to it. It's entirely possible that what you thought was a perfectly good "mathematical" solution -- mathematics is not always a matter of special knowledge and magical formulas!

But there may be a postulate or theorem you would have learned; did you have reference to such a thing as part of your thinking?

On the other hand, did you quote the problem exactly? I wouldn't expect a math question to say just "How many different planes are formed?", without saying by what!
Line j is a line. I just assumed this meant a linear line. So then I just imagined drawing a line. Then I thought that this line has 2 arbitrary points on it that are within and on the line itself. Then I did the same thing for another line. Then I knew that the two lines intersect so I just sorta made a line of an X in my head. One line is / and the other is \ and since they cross, and each line has two arbitrary points on each line, that's what I figured the answer was.

How to describe this mathematically, I really have no clue though.

6. Originally Posted by Dr.Peterson
Tell us what your answer is, and what your thoughts were that led you to it. It's entirely possible that what you thought was a perfectly good "mathematical" solution -- mathematics is not always a matter of special knowledge and magical formulas!

But there may be a postulate or theorem you would have learned; did you have reference to such a thing as part of your thinking?

On the other hand, did you quote the problem exactly? I wouldn't expect a math question to say just "How many different planes are formed?", without saying by what!
Well, Quick isn't the OP, but I guess everything you said above applies equally well to the OP.

7. Originally Posted by Quick
Line j is a line. I just assumed this meant a linear line. So then I just imagined drawing a line. Then I thought that this line has 2 arbitrary points on it that are within and on the line itself. Then I did the same thing for another line. Then I knew that the two lines intersect so I just sorta made a line of an X in my head. One line is / and the other is \ and since they cross, and each line has two arbitrary points on each line, that's what I figured the answer was.

How to describe this mathematically, I really have no clue though.
What you describe is essentially what j-astron suggested doing. Nothing non-mathematical about it, really, unless you were told to prove it. An intuitive understanding like this is "mathematical", just in a different sense -- and vitally important.

If you want a proof, have you learned something that says that two intersecting lines determine a plane? If not, what theorems HAVE you learned about planes?

The same goes for the OP, of course; I'm treating you as a stand-in.

8. Originally Posted by Dr.Peterson
What you describe is essentially what j-astron suggested doing. Nothing non-mathematical about it, really, unless you were told to prove it. An intuitive understanding like this is "mathematical", just in a different sense -- and vitally important.

If you want a proof, have you learned something that says that two intersecting lines determine a plane? If not, what theorems HAVE you learned about planes?

The same goes for the OP, of course; I'm treating you as a stand-in.
I am not sure what theorems I have learned about planes. The concepts of them are probably buried in my subconscious because I had to just look up what a plane actually was. I have taken algebra in the past and got as far as pre-calc in HS (a class I got a D in [I was depressed and a long story which is neither here nor there]), so I know some trig concepts as well, but it's all foggy stuff that I don't know the details of the concepts I might know.