Posted by **Anonymous** on Tuesday, January 11, 2011 at 3:31am.

an equation is being tested for symmetry with respect to the x-axis, the y-axis, and the origin. explain why, if two of these symmetries are present then remaining one must also be present.

- math -
**drwls**, Tuesday, January 11, 2011 at 8:31am
For x-axis reflection symmetry,

f(x,y) = f(x,-y)

For y-axis reflection symmetry,

f(x,y) = f(-x,y)

For symmetry about the origin,

f(x,y) = f(-x,-y)

If you reflect about both x and y axes, it is equivalent to reflecting about the origin.

If you reflect about the origin and then one axis, you have reflected about the other axis.

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