What does it mean when a graph or a point on the Cartesian plane is symmetric about the origin or with respect to the origin?
[Math] What does “symmetric about the origin” mean
graphing-functions
graphing-functions
What does it mean when a graph or a point on the Cartesian plane is symmetric about the origin or with respect to the origin?
Best Answer
That $f(-x)=-f(x)$ for all $x$.
Geometrically, this means that if you reflect the graph of $f$ about one axis and then the other, the graph will land back on top of itself (i.e., you'll get the original graph again).
Same idea with a point $P(x,y)$: $Q(-x,-y)$ would be the corresponding point symmetric about the origin.