The Coordinate Axes

• In mathematics, the notion of symmetry stems from the "x" and "y" coordinate axes. The coordinate axes are an arrangement of two lines that make a right angle with one another --- one vertical, the y-axis, and one horizontal, the x-axis. The origin is the point at which both lines crisscross. Each line contains equally spaced partitions or units that the mathematician uses to determine the values and measurements of graphs of functions.
  
  

Origin Symmetry

• Symmetry about the origin.Jupiterimages/Photos.com/Getty Images
  
  Mathematicians typically situate the axis to a circle by superimposing the origin of the axes on top of the center of the circle. This method of placement makes the equations of a circle much easier to manipulate because every point on the circle's edge is an identical distance from the origin. In this case, the circle possesses symmetry to the origin -- the circle's mirror image appears above and below the x-axis as well as to the left and right of the y-axis.
  
  

X-axis Symmetry

• Symmetry about the x-axis reveals a mirror image both above and below the horizontal axis running through the origin.Jupiterimages/Photos.com/Getty Images
  
  Some graphs contain a special property that makes them perfectly symmetric with the x-axis. The x-axis is horizontal on the coordinate axes and contains the unknowns or input values of a function. A graph is symmetric about the x-axis if its mirror image appears both above and below the x-axis. In mathematical terms, the function will produce identical "x" values on either side of the x-axis.
  
  

Y-axis Symmetry

• If a graph is identical on both sides of the vertical y-axis, it has symmetry about the y-axis.Thomas Northcut/Lifesize/Getty Images
  
  The y-axis is the vertical coordinate axis and contains the output values of a mathematical equation for all inputted y-values. Symmetry about the y-axis abides by the same principles as symmetry about the origin and symmetry about the x-axis. The only difference is that the graph's mirror image shows up on either side of the y-axis. Mathematically, it is the opposite of symmetry about the x-axis -- the function will produce identical "y" values on either side of the y-axis.