Line of Symmetry

Pronunciation: /laɪn ʌv ˈsɪm.ɪ.tri/ Explain
Click on the blue point and drag it to change the figure.

Note that the blue point on the line of symmetry is always the same distance from the sides of the parabola.
Manipulative 1 - Line of Symmetry of a Parabola Created with GeoGebra.

A line of symmetry is a line about which a geometric object or objects are reflection symmetrical. Manipulative 1 shows the line of symmetry of a parabola. If the parabola is reflected about this line of symmetry it remains unchanged.

A function may have an inverse. A function and its inverse are symmetrical around the line y = x. Manipulative 2 shows the function y = x2 / 4 and its inverse, y = (4x)1/3. Click on the light blue point labeled 'ClickNDrag' and drag it along the line y = x. Note that the line is equidistant from the function and its inverse.

Click on the blue point an drag it to change the figure

Note that the blue point on the line of symmetry is always equidistant from both functions.
Manipulative 2 - Line of Symmetry Between Inverse Functions Created with GeoGebra.


  1. McAdams, David E.. All Math Words Dictionary, line of symmetry. 2nd Classroom edition 20150108-4799968. pg 109. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. symmetry. Encyclopedia Britannica. Merriam-Webster. Last Accessed 8/31/2018. Buy the book

Cite this article as:

McAdams, David E. Line of Symmetry. 4/24/2019. All Math Words Encyclopedia. Life is a Story Problem LLC.

Image Credits

Revision History

4/24/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
8/31/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
10/11/2008: Initial version. (McAdams, David E.)

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