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. Note
that the reflected figure is a mirror image of the original
figure.
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.

How to Construct 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. 
How to Construct the Reflection of a Triangle
Step  Figure  Description 
1  
We will be constructing the reflection of triangle
ΔABC 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
ΔA'B'C' is the reflection of triangle
ΔABC across the line of reflection. 
Table 1: Constructing the reflection of a triangle. 
References
 McAdams, David E.. All Math Words Dictionary, reflection. 2nd Classroom edition 201501084799968. pg 153. Life is a Story Problem LLC. January 8, 2015. Buy the book
More Information
Cite this article as:
McAdams, David E. Reflection. 5/2/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/r/reflection.html.
Image Credits
Revision History
5/2/2019: Changed equations and expressions to new format. (
McAdams, David E.)
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.)