Reflections

Advanced GeometryRigid Transformations

Lesson 2

Reflection

Line of Reflection

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Pre-image Image

P

EN

T A

P

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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

BC

trapezoid FHGA

D

BA

.l

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

thefigure has point symmetry.

A point of symmetry is the midpoint of all line segments joining opposite points of the figure.