# 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
StepFigureDescription
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
StepFigureDescription
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.
1. McAdams, David E.. All Math Words Dictionary, reflection. 2nd Classroom edition 20150108-4799968. pg 153. Life is a Story Problem LLC. January 8, 2015. Buy the book

McAdams, David E. Reflection. 5/2/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/r/reflection.html.

### 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.)