Reflection
Pronunciation: /rɪˈflɛk.ʃən/ Explain
Click on the blue points and drag them to change the figure.
What happens if the line of reflection intersects the objects being reflected?
 Manipulative 1  Reflection Across a Line Created with GeoGebra. 

A reflection is a geometric transformation. In a
reflection, a geometric object is 'flipped' across a
line. The line across which an object is reflected is called the
line of reflection or the
axis of reflection.
Manipulative 1 shows the reflection of an irregular pentagon across a line.
Click on the blue points in manipulative 1 and drag them to change the figure. Note
that the reflected figure is a mirror image of the original
figure. To see the construction of A' and B', click on the
check boxes.
Properties of Reflections
 An object and its reflection are symmetrical about the line of reflection.
 An object and its reflection are
congruent.
 An object and its reflection are
similar.
 If a reflected object is reflected again about the same line of reflection,
the resulting object is
coincidental
with the original object.

Constructing a Reflection
Constructing the Reflection of a Point
Step  Figure  Description 
1   We will be constructing the reflection of point A across the line of reflection. 
2   Construct a line perpendicular to the line of reflection that passes through point A. 
3   Mark the intersection of the perpendicular lines as P. 
4   Use a compass with the point on P and the stylus on point A. Without removing the point from P, draw a circular arc on the opposite side of the perpendicular line. 
5   Mark the intersection of the arc and the perpendicular line as A'. 
Table 1: Constructing the reflection of a point. 
Constructing the Reflection of a Triangle
Step  Figure  Description 
1   We will be constructing the reflection of triangle ?ABC across the line of reflection. 
2   Construct the reflection of A across the line of reflection (see table 1). Label the reflected point A'. 
3   Construct the reflection of B across the line of reflection. Label the reflected point B'. 
4   Construct the reflection of C across the line of reflection. Label the reflected point C'. 
5   Use a straight edge to connect points A', B' and C' with line segments. The triangle ?A'B'C' is the reflection of triangle ?ABC across the line of reflection. 
Table 1: Constructing the reflection of a triangle. 
More Information
Cite this article as:
McAdams, David E. Reflection. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/r/reflection.html.
Image Credits
Revision History
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
12/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra app. (
McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (
McAdams, David E.)
1/13/2009: Initial version. (
McAdams, David E.)