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How do I determine if a plane is even with respect to an axis? 
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#1
Dec313, 04:12 PM

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I know that the plane ##z=4y## is even with respect to the xaxis and is not even with respect to the yaxis and zaxis from graphing the plane.
How would I algebraically determine this? 


#2
Dec313, 05:21 PM

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



#3
Dec313, 05:28 PM

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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 yz plane. Each point is directly across the yz 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 xz 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 zaxis. I'll let you figure out what it means for a surface to have symmetry about the other two axes. 


#4
Dec313, 05:31 PM

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How do I determine if a plane is even with respect to an axis?
The volume under the plane from both sides of the xaxis is the same but this is not the case for the yaxis and zaxis. 


#5
Dec313, 06:21 PM

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