Reflection

Pronunciation: /rɪˈflɛk ʃən/ Explain

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Manipulative 1: Reflection. 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
StepFigureDescription
1A line of reflection and a point A not on the line of reflection.We will be constructing the reflection of point A across the line of reflection.
2A line of reflection and a point A not on the line of reflection. A line perpendicular to the line of reflection passing through point A has been drawn.Construct a line perpendicular to the line of reflection that passes through point A.
3A line of reflection and a point A not on the line of reflection. A line perpendicular to the line of reflection passing through point A has been drawn. The intersection of the two lines is marked as point P.Mark the intersection of the perpendicular lines as P.
4A line of reflection and a point A not on the line of reflection. A line perpendicular to the line of reflection passing through point A has been drawn. The intersection of the two lines is marked as point P. Two arcs on the circle with center at point P and radius of PA have been drawn that intersect the perpendicular line.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.
5A line of reflection and a point A not on the line of reflection. A line perpendicular to the line of reflection passing through point A has been drawn. The intersection of the two lines is marked as point P. Two arcs on the circle with center at point P and radius of PA have been drawn that intersect the perpendicular line. The intersection of the arc opposite point A and the perpendicular line is marked A'.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
StepFigureDescription
1A line of reflection and a triangle ABC.We will be constructing the reflection of triangle ?ABC across the line of reflection.
2A line of reflection and a triangle ABC. Point A' is the reflection of A across the line of reflection.Construct the reflection of A across the line of reflection (see table 1). Label the reflected point A'.
3A line of reflection and a triangle ABC. Point B' is the reflection of B across the line of reflection.Construct the reflection of B across the line of reflection. Label the reflected point B'.
4A line of reflection and a triangle ABC. Point C' is the reflection of C across the line of reflection.Construct the reflection of C across the line of reflection. Label the reflected point C'.
5A line of reflection and a triangle ABC. Points A', B' and C' are connected with line segments forming triangle A'B'C'.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. 5/5/2011. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/r/reflection.html.

Image Credits

Revision History

1/13/2009: Initial version. (McAdams, David E.)

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