topic: u6l3 translations and rotations
DESCRIPTION
Topic: U6L3 Translations and Rotations. EQ: Can I demonstrate an understanding of translations and rotations , reflections, and relate symmetry to appropriate transformations?. In geometry, a transformation is a way to change the position of a figure. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/1.jpg)
Topic: U6L3 Translations and Rotations
EQ: Can I demonstrate an understanding of translations and rotations, reflections, and
relate symmetry to appropriate transformations?
![Page 2: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/2.jpg)
In geometry, a transformation is a way to change the position
of a figure.
![Page 3: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/3.jpg)
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.
![Page 4: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/4.jpg)
TRANSLATION
![Page 5: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/5.jpg)
TRANSLATIONA 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.
![Page 6: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/6.jpg)
TRANSLATIONBasically, 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.
![Page 7: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/7.jpg)
TRANSLATIONWhat does a translation look like?
A TRANSLATION IS A CHANGE IN LOCATION.
x yTranslate from x to y
original image
![Page 8: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/8.jpg)
TRANSLATIONIn the example below triangle A is translated to
become triangle B.
A B
Describe the translation.Triangle A is slide directly to the right.
![Page 9: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/9.jpg)
TRANSLATIONIn 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
![Page 10: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/10.jpg)
ROTATION
![Page 11: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/11.jpg)
ROTATIONA rotation is a transformation that turns a figure about (around) a point or a line.
The point a figure turns around is called the center of rotation.
Basically, rotation means to spin a shape.
The center of rotation can be on or outside the shape.
![Page 12: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/12.jpg)
ROTATIONWhat does a rotation look like?
A ROTATION MEANS TO TURN A FIGURE
center of rotation
![Page 13: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/13.jpg)
ROTATIONThis is another way rotation looks
A ROTATION MEANS TO TURN A FIGURE
The triangle was rotated around the
point.
center of rotation
![Page 14: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/14.jpg)
ROTATIONIf a shape spins
360, how far does it spin?
All the way around
This is called one full turn.
360
![Page 15: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/15.jpg)
ROTATIONIf a shape spins
180, how far does it spin?
Half of the way around
This is called a ½ turn. 180
Rotating a shape 180 turns a shape upside down.
![Page 16: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/16.jpg)
ROTATIONIf a shape spins 90,
how far does it spin?
One-quarter of the way around
This is called a ¼ turn.
90
![Page 17: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/17.jpg)
ROTATIONDescribe how the triangle A was transformed to
make triangle B
A B
Describe the translation.Triangle A was rotated right 90
![Page 18: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/18.jpg)
ROTATIONDescribe how the arrow A was transformed to make
arrow B
Describe the translation.Arrow A was rotated right 180
A
B
![Page 19: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/19.jpg)
ROTATIONWhen some shapes are rotated they
create a special situation called rotational symmetry.
to spin a shape the exact same
![Page 20: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/20.jpg)
ROTATIONAL SYMMETRYA 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…
As this shape is rotated 360, is it ever the same before the shape returns to
its original direction?Yes, 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
![Page 21: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/21.jpg)
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?Yes, 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.
![Page 22: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/22.jpg)
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 360 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.
![Page 23: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/23.jpg)
ROTATION SYMMETRYDoes 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
![Page 24: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/24.jpg)
CONCLUSIONWe just discussed two of the four types of
transformations.
See if you can match the action with the appropriate transformation.
SLIDETURN
TRANSLATIONROTATION
![Page 25: Topic: U6L3 Translations and Rotations](https://reader035.vdocuments.net/reader035/viewer/2022062520/568161d9550346895dd1e1b5/html5/thumbnails/25.jpg)
Translations and rotations change the position of a shape, while the size
remains the same.