MHB Is This Equation Symmetric About the Origin?

[mathdad]

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?

 

[MarkFL]

I agree there is no symmetry about the axes, however:

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

Hence, this is symmetric about the origin.

 

[mathdad]

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!