MHB Is This Equation Symmetric About the Origin?

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The equation |x + y| = 2 is tested for symmetry about the x-axis, y-axis, and the origin. It is determined that the equation is not symmetric about the y-axis or the x-axis. However, the discussion reveals that it is symmetric about the origin, as shown by the transformation |(-x) + (-y)| = |x + y|. This conclusion highlights that while there is no symmetry about the axes, the equation retains symmetry about the origin. The final agreement confirms the equation's origin symmetry.
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Test for symmetry about the x-axis, y-axis and the origin.

|x + y| = 2

About y-axis:

|-x + y| = 2

Not symmetric about y-axis.

About x-axis:

|x + -y| = 2

I say not symmetric about the x-axis.

About the origin:

|-x + -y| = 2

Not symmetric about the origin.

Correct? If not, why?
 
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I agree there is no symmetry about the axes, however:

$$|(-x)+(-y)|=|-(x+y)|=|x+y|$$

Hence, this is symmetric about the origin.
 
MarkFL said:
I agree there is no symmetry about the axes, however:

$$|(-x)+(-y)|=|-(x+y)|=|x+y|$$

Hence, this is symmetric about the origin.

Nicely done!
 
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