# Symmetry

Monday, April 9th, 2012 at
12:09 pm

# Symmetry

## The graph of an equation may be symmetrical over the x-axis, the y-axis and/or the origin. Knowing if a graph is symmetrical helps make it easier to sketch the graph of an equation.

## To test for x-axis symmetry, you need to replace y with –y. If the new equation is identical to the original equation, then the graph is symmetrical over the x-axis.

## To test for y-axis symmetry, you replace x with –x. If the new equation is identical to the original equation, then the graph is symmetric over the y-axis.

## To test for symmetry over the origin, you replace x with –x, and y with –y. Again if the equation is identical to the original equation, then the graph is symmetric over the origin.

## The linear equations y = x or y = -x are the only two equations which are symmetric over the origin.

## The equation for a circle with centre (0.0) is symmetric over the x-axis, the y-axis and the origin.

**Filed under: **Functions and Their Graphs

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