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

  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. SteamKing

    SteamKing 8,860
    Staff Emeritus
    Science Advisor
    Homework Helper

    What do you mean by 'even w.r.t. an axis'?
     
  4. 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.
     
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  5. 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. 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.
     
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