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

In summary, the conversation discusses the concept of symmetry in relation to a plane with the equation z=4-y. It is mentioned that the plane is even with respect to the x-axis, but not with respect to the y-axis and z-axis. The conversation also explores the difference between symmetry across a plane and symmetry about an axis. It is noted that the volume under the plane is equal on both sides of the x-axis, but not on the y-axis and z-axis due to the plane's lack of symmetry.
  • #1
ainster31
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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?
 
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  • #2
What do you mean by 'even w.r.t. an axis'?
 
  • #3
ainster31 said:
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?

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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  • #4
SteamKing said:
What do you mean by 'even w.r.t. an axis'?

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.
 
  • #5
ainster31 said:
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.
You are not describing the image correctly. The solid is symmetric across the y-z plane. I described this in my previous post.
 

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

The best way to determine if a plane is even with respect to an axis is to use a level or a plumb line. Place the level or plumb line on the plane and adjust it until the bubble is centered or the line is vertical. If the bubble is centered or the line is vertical, the plane is even with respect to the axis.

2. What is the importance of determining if a plane is even with respect to an axis?

Determining if a plane is even with respect to an axis is important because it ensures that the plane is level and will not cause any imbalances or inaccuracies in measurements. It is also important for safety reasons, as an uneven plane can lead to accidents or equipment failures.

3. Can I use a ruler or measuring tape to determine if a plane is even with respect to an axis?

No, using a ruler or measuring tape is not an accurate way to determine if a plane is even with respect to an axis. These tools may not be precise enough to detect small variations in the plane's level. It is best to use a level or plumb line for this task.

4. How do I know which axis to use when determining if a plane is even?

The axis to use will depend on the orientation of the plane. If the plane is horizontal, the axis to use would be the vertical axis. If the plane is vertical, the axis to use would be the horizontal axis. It is important to use the correct axis to get an accurate reading.

5. Are there any other methods for determining if a plane is even with respect to an axis?

Yes, there are other methods such as using a laser level or a digital inclinometer. These tools provide more precise and accurate measurements and can be useful for more complex or delicate tasks. However, for most general purposes, a simple level or plumb line will suffice.

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