Reflection symmetry is also called line symmetry, or mirror symmetry. Both halves of the object are mirror images of one another. The line of symmetry, called the mirror line, may be in any direction, and there may be more than one. The four lines of symmetry for a square are located at the horizontal and vertical halves, and at both diagonal halves. A circle has an infinite number of lines of symmetry, as long as a straight line at any angle passes through the center of the circle.
Shapes or images that are rotated -- moved around on an axis -- and retain their shape have rotational symmetry. A two-blade propeller will look the same two times for every one rotation. Each match is called an order, so a two-blade propeller has rotational symmetry of "order 2." If you marked one blade to identify it and rotated the blade halfway around on its axis, it would look the same as when you started. Move it halfway around again to complete a rotation, and it still appears the same.
Every part of a shape or image with point -- or origin -- symmetry has a matching part in the opposite direction, located the same distance from the origin, also called the central point. It will look the same from opposite directions. Playing cards frequently display point symmetry; they look the same from opposite directions. If you cut one in half at a 45-degree angle and put both halves in the same direction, they will be an exact match. Other examples include the uppercase letters "H," "I," "N," "S," "X" and "S."
When a shape or image is moved without rotation or reflection, it has translation symmetry. Its position is changed in direction and distance.
An image or shape with glide reflection symmetry is translated -- or moved -- along the mirror line, then reflected. It is the only type of symmetry that takes two steps.
Symmetry in equations is easy to see when plotted on an x-axis and y-axis, but it should be checked to verify the equation is unchanged when using symmetric values. Substitute "-x" for "x" to check for symmetry in the y-axis. For the x-axis, substitute "-y" for "y." To check for diagonal symmetry, substitute "x" for "y," and "y" for "x." An equation has origin symmetry if you can replace "x" with "-x," and "y" with "-y."