Results 1 to 8 of 8

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

  1. #1

    Question 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
    D) Cannot be determined (as more info is needed)


    Can you please provide a brief explanation? Thanks!

  2. #2
    Junior Member
    Join Date
    Jan 2018
    Location
    Toronto
    Posts
    66
    Quote Originally Posted by I am bad at quick maths View Post
    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
    D) Cannot be determined (as more info is needed)


    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. #3
    Junior Member
    Join Date
    Jan 2018
    Posts
    85
    I get the answer to this question, but I have no idea how to slove it mathematically...

  4. #4
    Full Member
    Join Date
    Nov 2017
    Location
    Rochester, NY
    Posts
    599
    Quote Originally Posted by Quick View Post
    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. #5
    Junior Member
    Join Date
    Jan 2018
    Posts
    85
    Quote Originally Posted by Dr.Peterson View Post
    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. #6
    Junior Member
    Join Date
    Jan 2018
    Location
    Toronto
    Posts
    66
    Quote Originally Posted by Dr.Peterson View Post
    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. #7
    Full Member
    Join Date
    Nov 2017
    Location
    Rochester, NY
    Posts
    599
    Quote Originally Posted by Quick View Post
    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. #8
    Junior Member
    Join Date
    Jan 2018
    Posts
    85
    Quote Originally Posted by Dr.Peterson View Post
    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.

Tags for this Thread

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •