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Advanced Geometry Rigid Transformations Lesson 2

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Reflections

Advanced Geometry

Rigid Transformations

Lesson 2

flip

Line of Reflection

http://www.mathsisfun.com/flash.php?path=%2Fgeometry/images/reflection.swf&w=670.5&h=579&col=%23FFFFFF&title=Geometry+-+Reflection

Pre-image

Image

N

E

E

N

P

P

T

A

A

T

Example:

Draw the reflected image of quadrilateral WXYZ

in line p.

Example:

Name the image of each figure under a

reflection in line

F

D

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.