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Name _____________________________________________ Date: ________________
Guided Notes: Transformation Unit
Transformation: a change in a figures position, shape, or size.
 Can flip, slide, or turn
 Preimage: the original figure
 Image: the resulting figure
Isometry: a transformation in which the preimage and the image are congruent (also
called Rigid Transformations)
Composition of Transformations: combination of 2 or more transformations
Notation:
𝐴 → 𝐴′
(𝐴 maps onto 𝐴′ )
𝐴′ would be the image of 𝐴
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Translations: [SLIDE]
 Slides all the points in the plane the same distance in the same direction.
 This has no effect on the size of the figures in the plane.
Coordinate Notation: (𝑥, 𝑦) → (𝑥 ± 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥, 𝑦 ± 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦)
To write a rule for a translation:
 Calculate the horizontal change from preimage
to image (change in 𝑥 values)
 Calculate the vertical change from preimage to
image (change in 𝑦 values)
How would you write a rule for the translation shown above?
Example #1
Graph the image of the figure using the transformation given. Label the new coordinates.
How would you write the rule using coordinate notation?
Preimage
Image
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Reflections: [FLIP]
 A reflection flips all the points in the plane over a line.
 A figure and its image have opposite orientation.
To find the coordinates of the reflection:
 To reflect over the line 𝑦 = 𝑥, interchange 𝑥 and 𝑦 coordinates
 To reflect over the 𝑥 −axis, multiply the 𝑦 −coordinate by – 1
 To reflect over the 𝑦 −axis, multiply the 𝑥 −coordinate by – 1
 To reflect about the origin, multiply both coordinates by −1
Example #2
Reflection across 𝑦 = 2
Example #3
Reflection across 𝑥 − 𝑎𝑥𝑖𝑠
Example #4
Reflection across 𝑥 = −2
Example #5
Reflection across 𝑦 = 𝑥
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Rotations: [TURN]
 Turns all the points in the plane around one point, which is called the center of rotation.
A rotation does not change the size of figures in the
plane.
 A rotation of 180 degrees is called a half-turn
 A rotation of 90 degrees is called a quarter turn.
Need to know:
1. Center of rotation
2. Angle of rotation
3. Whether the rotation is clockwise or counterclockwise (assume counterclockwise unless
otherwise stated)
Rules for Rotations where the center of rotation is (𝟎, 𝟎) (counterclockwise)
COUNTER
CLOCKWISE
PREIMAGE
[Before]
IMAGE
[After]
NOTE:
**If it is a clockwise rotation for 𝟗𝟎°,
use the 𝟐𝟕𝟎° rule
90°
(𝑥, 𝑦)
(−𝑦, 𝑥)
180°
(𝑥, 𝑦)
(−𝑥, −𝑦)
270°
(𝑥, 𝑦)
(𝑦, −𝑥)
Example #6
**If it is a clockwise rotation for 𝟐𝟕𝟎°,
use the 𝟗𝟎° rule
Example #7
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Symmetry:
A figure has symmetry if there is an isometry that maps a figure onto itself. If a figure looks the
same under a transformation then it is said to be symmetrical under that transformation.
Reflectional or Line Symmetry:
 Isometry is the reflection of a plane figure
 One-half of the figure is a mirror image of its other half
Rotational Symmetry:
 A figure that has rotational symmetry is its own image for some rotation of 180 degrees
or less.
 A figure that has Point Symmetry has 180 degree rotational symmetry.
Example: a square has rotational and point symmetry
Dilations: [GROW or SHRINK]
 Preimage and image are similar, not congruent
 Not an isometry (not a rigid transformation)
 The figure is enlarged or reduced by a scale factor
Scale Factor: describes the size change from original figure to the image
Enlargement: scale factor is greater than 1
Reduction: scale factor is between 0 and 1
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Example #8
Graph the dilated image of quadrilateral MNOP using a scale factor of 1/3 and the origin as
the center of dilation.
Example #9
Graph the dilated image of triangle JKL using a scale factor of 2 and the origin as the center
of dilation.