Symmetry

Today I'll be teaching how to check for symmetry. You can check for symmetry about the x-axis, y-axis, the origin, and line y=x.

To check for symmetry about the x-axis you must:

• put a (-) in front of the y's and simplify.


• if it matches the original problem then it is symmetry about the x-axis

To check for symmetry about the y-axis you must:

• plugin a (-) in front of the x's and simplify


• if it matches the original problem then it is symmetry about the y-axis

To check for symmetry about the origin you must:

• plugin a (-) in front of the x's and y's then simplify


• if it matches the original equation then it is symmetry about the origin

To check for symmetry about line y=x you must:

• switch the x's with the y's and solve for y


• if it matches the original equation then it is symmetry about line y=x

Example 1: y^2+xy=5

i. (-y)^2+x-y=5

-y^2-xy=5

no

ii. y^2+-xy=5

y^2-xy=5

no

iii. -y^2-x-y=5

-y^2+xy=5

no

iv. x^2+yx=5

no