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Problem 7

$7-8=$ Yes or $N o ?$ If $N o,$ give a reason.

If the graph of an equation is symmetric with respect to both

the $x$ - and $y$ -axes, is it necessarily symmetric with respect to

the origin?

Answer

Yes

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## Discussion

## Video Transcript

this question asks if graph of of an equation symmetric with respect both the X and Y axes Is it necessarily symmetric with respect to the origin? And the answer is yes. Let me explain if the graph oven equation is symmetric with respect to the X axis and that means that for a given point a B point a negative B is also on the graph. If it is symmetric with respect to the Y axis, then for that given point a b the point negative A B is also on the axis. No note, please, for symmetry with respect to the origin. If the point a b is on the graph than the point negative, a negative B is on the graph noticed that both conditions from the X and Y axis symmetry tests are involved in the origin symmetry, so therefore the answer is yes.

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