SymmetrySmoke and mirrors

Types of Symmetry

X-axis symmetry

Y-axis symmetry

Origin symmetry

X-axis Symmetry

If both (a,b) and (a,-b) are on the graph.

A graph will have symmetry about the x-axis if we get an equivalent equation when all the y’s are replaced with -y.

Basically if the graph is mirrored over the x-axis then it is x-axis symmetry.

Y-axis Symmetry

If both (a,b) and (-a,b) are on the graph.

A graph will have symmetry about the y-axis if we get an equivalent equation when all the x’s are replaced with -x.

Basically if the graph is mirrored over the y-axis then it is y-axis symmetry.

Origin Symmetry

If both (a,b) and (-a, -b) are on the graph

The graph will have origin symmetry if all the x’s where replaced with –x, then the y’s would become –y.

Basically if the image is rotated about the origin 180⁰, then it has origin symmetry.