Transformations

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Transformations
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transformation

• One to One Mapping
• Preimage Point ? Image Point

A ? A

• A change of position or size of a figure.

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reflections

• The mirror image of the original figure

The figures are congruent!
The original image is flipped!
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Example
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The line of Reflection is also called the line of
symmetry.
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It is also possible to have a reflection image
with respect to a point.
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Point of Symmetry

• The point must be the midpoint for all segments
  that pass through it and have endpoints on the
  figure.

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Example
Does Rhombus MATH have point symmetry?
Yes
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translation

• A transformation that moves points the same
  distance and in the same direction.

The figures are congruent!
Often referred to as a glide!
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Example
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Translations are a composite of Reflections

• One reflection over another with respect to two
  parallel lines.

l
m
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rotation

• A transformation that turns a figure about a
  fixed point.

Example
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Another Example
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Rotations are a composite of Reflections

• One reflection over another with respect to two
  intersecting lines.

Not drawn to scale!
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Center of rotation

• The measure of the angle of rotation is twice the
  measure of the angle formed by the intersecting
  lines
• Turn around Point

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dilation

• Alters the size of a geometric figure, but does
  not change its shape.

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isometry

• Congruence Transformation
• Maps every segment to a congruent segment
• No change in size!
• Congruent sides and congruent angles

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State whether each of the following have isometry.

• Translation
• Reflection
• Rotation
• Dilation

Yes
Yes
Yes
No