Honors Geometry Transformations
Section 1
Reflections
A transformation is a movement of
a figure in a plane from its original
position to a new position.
The original figure is called the
preimage , while the figure resulting
from the transformation is called
the image . A point in the image is
usually named by adding a prime
symbol (  ) to the name of the
point in the preimage.
In a rigid transformation, or
isometry, the image is congruent to
the preimage.
We will consider three basic
isometries: translations, reflections
and rotations.
A reflection in a line m (or flip over
line m) is a transformation that maps
(or matches up) any point P to a point P 
so that these two properties are true.
1. If P is not on m, then
PP  m and m bisects PP
2. If P is on m, then
P  P
Let’s take a look at reflections in
the coordinate plane.
Example 1: Consider reflecting point A(3, 5) in
the given line. Give the coordinate of its image.
A
(3, 5)
a) x-axis ________
(3,5)
b) y-axis ________
3)
c) the line y = 1 (3,
_______


7,5
d) the line x = -2 ________
e) the line y = x (5,3)
_______
3, 1)
f) the line y=-x+2 (_____
g) the line y = x - 1 _____
e) the line y = x (5,3)
_______
3, 1)
f) the line y=-x+2 (_____
 6, 2 
g) the line y = x - 1 _____
A figure has a line of symmetry if
the figure can be mapped onto
itself by a reflection in a line.
The previous statement is the
formal definition of a line of
symmetry, but it is much easier to
think of a line of symmetry as the
line where the figure can be folded
and have the two halves match
exactly.
Example 2: Draw all lines of symmetry.
Example 3: Name two capital
letters that have exactly two lines
of symmetry.
H I O X