Advanced Geometry
Rigid Transformations
Lesson 2
Reflections
Reflection
flip
Line of Reflection
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on.swf&w=670.5&h=579&col=%23FFFFFF&title=Geometry+-+Reflection
Pre-image
Image
N
E
N
A
T
E
P
T
A
P
Example:
Draw the reflected image of quadrilateral WXYZ
in line p.
Example:
Name the image of each figure under a
reflection in line l .
F
BC
D
BA
trapezoid FHGA
Example:
Quadrilateral ABCD has vertices A(1, 1), B(3, 2),
C(4, -1), and D(2, -3). Graph ABCD and its image
under reflection in the x-axis.
Example:
Triangle RST has vertices R( -1, 3), S(-5, -2),
and T(2, 4). Graph RST and its image under
reflection in the y-axis.
Example:
Quadrilateral RUDV has vertices R(-2, 2), U(3, 1),
D(4, -1), and V(-2, -2) and is reflected in the origin.
Graph RUDV and its image.
To reflect
in the
origin, reflect
over both the
x-axis AND
y-axis.
Example:
Triangle XYZ has vertices X(4, -2), Y(2, -3),
and Z(3, -5). Graph XYZ and it image under
reflection in the line y = x.
Example:
Rectangle JKLM has vertices J(0, 2), K(0, -2),
L(3, 2), and M(3, -2). Graph JKLM and its
image under reflection in the line y = -x.
If a figure can be folded so that the two halves
match exactly, the fold is called a line of symmetry.
For some figures, a common point of symmetry,
called a point of reflection, exists
for all points on a figure
Example:
Determine how many lines of symmetry the figure
has and draw them. Then determine whether the
figure has point symmetry.
A point of symmetry is the midpoint of all line
segments joining opposite points of the figure.