This document discusses different types of geometric transformations including translations, rotations, reflections, and dilations. It provides examples and definitions for each type of transformation. Translations involve sliding a figure across a plane without changing its size or shape. Rotations involve turning a figure around a central point. Reflections involve flipping a figure across a line to create a mirror image. Some shapes exhibit rotational or reflectional symmetry if applying one of those transformations results in an identical configuration.

1. TRANSFORMATIONS-I
(TRANSLATIONS, ROTATIONS,
REFLECTIONS, AND DILATIONS)
Math 103
GEOMETRY
Dr. Farhana Shaheen

2. OBJECTIVES: TRANSFORMATION
 Demonstrate understanding of:
 1. Translations
 2. Rotations
 3. Reflections
 4. Dilations
 Relate symmetry to appropriate transformations.
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3. In geometry, a transformation is a
way to change the position of a
figure.
Transformation
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Types of Transformations
Translations, Rotations, Reflections, and
Dilations

5. Transformation is a way to change.
Transformation in Real life
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6. In some transformations, the figure
retains its size and only its position is
changed.
Examples of this type of transformation
are:
translations, rotations, and reflections
In other transformations, such as
dilations, the size of the figure will
change.
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8. TRANSLATION
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9. TRANSLATION
A translation is a transformation that
slides a figure across a plane or through
space.
With translation all points of a figure move the same
distance and the same direction.
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10. TRANSLATION
Basically, translation means that a figure
has moved.
An easy way to remember what
translation means is to remember…
A TRANSLATION IS A CHANGE IN LOCATION.
A translation is usually specified by a
direction and a distance.
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11. TRANSLATION
What does a translation look like?
A TRANSLATION IS A CHANGE IN
LOCATION.
x y
Translate from x to y
original image
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12. TRANSLATION
In the example below triangle A is translated to
become triangle B.
A B
Describe the translation.
Triangle A is slide directly to the right.
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13. TRANSLATION
In the example below arrow A is translated to
become arrow B.
Describe the translation.
Arrow A is slide down and to the right.
A
B
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15. Example: 1 GUESS THE TRANSFORMATION?
How did you get it?
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19. REFLECTION
A REFLECTION IS FLIPPED OVER A LINE.
A reflection is a transformation that flips
a figure across a line.
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20. REFLECTION
A REFLECTION IS FLIPPED OVER A LINE.
After a shape is reflected, it looks like a
mirror image of itself.
Remember, it is the same, but
it is backwards
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REFLECTION

22. REFLECTION
The line that a shape is flipped over is
called a line of reflection.
A REFLECTION IS FLIPPED OVER A LINE.
Line of reflection
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23. REFLECTION
Determine if each set of figures shows a reflection or a
translation.
A REFLECTION IS FLIPPED OVER A LINE.
A
BC
A’
B’C’
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REFLECTION over x-axis

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REFLECTION over y-axis
(x, y) ------- (-x, y)

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REFLECTION in the line y=x
(x, y) ------- (y, x)

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29. REFLECTION
Sometimes, a figure has
reflectional symmetry.
This means that it can be folded along a line of
reflection within itself so that the two halves of the
figure match exactly, point by point.
Basically, if you can fold a shape in half and it
matches up exactly, it has reflectional symmetry.
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30. REFLECTIONAL SYMMETRY
An easy way to understand reflectional symmetry is to
think about folding.
Do you remember
folding a piece of
paper, drawing half
of a heart, and then
cutting it out?
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31. REFLECTIONAL SYMMETRY
How many lines of symmetry does each shape have?
Do you see a pattern?
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32. REFLECTIONAL SYMMETRY
Which of these flags have reflectional symmetry?
United States of America
Mexico
Canada
England
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33. ROTATION
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34. ROTATION
A rotation is a transformation that turns a
figure about (around) a point or a line.
Basically, rotation means to spin a shape.
The point a figure turns around is called the center
of rotation. The center of rotation can be on or
outside the shape.
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35. ROTATION
What does a rotation look like?
A ROTATION MEANS TO TURN A
FIGURE
center of rotation
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36. ROTATION
This is another way rotation looks
A ROTATION MEANS TO TURN A
FIGURE
The triangle
was rotated
around the
point.
center of rotation
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37. ROTATION
If a shape spins
360, how far does
it spin?
This is called
.
360
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38. ROTATION
If a shape spins 90,
how far does it
spin?
This is called a
.
90
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42. ROTATION
If a shape spins
180, how far does
it spin?
This is called a . 180
Rotating a shape 180
turns a shape upside
down.
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43. ROTATION
If a shape spins
270 clockwise,
how far does it
spin?
This is called a
.
270
Rotating a shape 270
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(Anti-clockwise ROTATION)

46. ROTATION
Describe how the triangle A was transformed to
make triangle B
A B
Describe the translation.
Triangle A was rotated right 90
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47. ROTATION
Describe how the arrow A was transformed to make
arrow B
Arrow A was rotated right 180
A
B
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48. ROTATION
When some shapes are rotated they
create a special situation called
rotational symmetry.
to spin a shape the exact same
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49. ROTATIONAL SYMMETRY
A shape has rotational symmetry if, after
you rotate less than one full turn, it is the
same as the original shape.
Here is an example…
If this shape is rotated 360, is it ever
the same before the shape returns to
its original direction?
When it is rotated 90 it is the same
as it was in the beginning.
So this shape is said to have
rotational symmetry.
90
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50. ROTATIONAL SYMMETRY
Here is another example…
As this shape is rotated 360, is it
ever the same before the shape
returns to its original direction?
When it is rotated 180 it is the
same as it was in the beginning.
So this shape is said to have
rotational symmetry.180
A shape has rotational symmetry if, after
you rotate less than one full turn, it is the
same as the original shape.
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51. ROTATIONAL SYMMETRY
Here is another example…
As this shape is rotated 360, is it
ever the same before the shape
returns to its original direction?
No, when it is rotated 180 it is
never the same.
So this shape does NOT have
rotational symmetry.
A shape has rotational symmetry if, after
you rotate less than one full turn, it is the
same as the original shape.
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52. ROTATION SYMMETRY
Does this shape have rotational symmetry?
120
Yes, when the
shape is rotated
120 it is the
same. Since 120 
is less than 360,
this shape HAS
rotational
symmetry
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54. CONCLUSION:
 A rotation is the turning of a figure or object around
a fixed point.
 And a translation is a scenario where every point
in a figure is moved the exact same distance and in
the same exact direction, without
being rotated, reflected, or resized.
 Translations Reflections and Rotations - YouTube
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56. CONCLUSION
We just discussed three types of transformations.
See if you can match the action with the
appropriate transformation.
FLIP
SLIDE
TURN
REFLECTION
TRANSLATION
ROTATION
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