1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How do I determine if a plane is even with respect to an axis?

  1. Dec 3, 2013 #1
    I know that the plane ##z=4-y## is even with respect to the x-axis and is not even with respect to the y-axis and z-axis from graphing the plane.

    How would I algebraically determine this?
     
  2. jcsd
  3. Dec 3, 2013 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    What do you mean by 'even w.r.t. an axis'?
     
  4. Dec 3, 2013 #3

    Mark44

    Staff: Mentor

    By "even" do you mean "symmetric"?

    Assuming that's what you mean, then if the points (x, y, z) and (-x, y, z) are both on a given surface, then the surface has symmetry across the y-z plane. Each point is directly across the y-z plane from the other. Similarly, if the points (x, y, z) and (x, -y, z) are both on a surface, then the surface has symmetry with respect to the x-z plane.

    Symmetry about an axis is different, because we're not talking mirror images any more. If the points (x, y, z) and (-x, -y, z) are both on a surface, then the surface is symmetric about the z-axis. I'll let you figure out what it means for a surface to have symmetry about the other two axes.
     
  5. Dec 3, 2013 #4
    http://i.imgur.com/Y9PfN4b.png

    The volume under the plane from both sides of the x-axis is the same but this is not the case for the y-axis and z-axis.
     
  6. Dec 3, 2013 #5

    Mark44

    Staff: Mentor

    You are not describing the image correctly. The solid is symmetric across the y-z plane. I described this in my previous post.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook