1. Rotations and Dilations

2. ROTATION
ROTATION

3. 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.
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, outside or even inside the shape.
The center of rotation can be on, outside or even inside the shape.

4. What does a rotation look like?
center of rotation
ROTATION
What does a rotation look like?
A ROTATION MEANS TO TURN A FIGURE
A ROTATION MEANS TO TURN A FIGURE

5. This is another way rotation looks.
The triangle was rotated around the point.
center of rotation
The triangle was rotated around the point.
This is another way rotation looks.
A ROTATION MEANS TO TURN A FIGURE
This is another way rotation looks.
A ROTATION MEANS TO TURN A FIGURE

6. ROTATION
Describe how the triangle A was transformed to make triangle B
Describe how the triangle A was transformed to make triangle B
Triangle A was rotated right 90 A B
Triangle A was rotated right 90
Describe the translation.

7. ROTATION Describe how the arrow A was transformed to make arrow B B A
Arrow A was rotated 180
Arrow A was rotated 180
Describe the translation.

8. Rotations with the Origin as the Center

9. 90o Clockwise Rotation About the Origin:

10. 90o Counterclockwise Rotation about the Origin

11. 180o Rotation Clockwise or Counterclockwise about the Origin

12. Rotations by Another Name
A 270o clockwise rotation about the origin is the same effect as a 90o counterclockwise rotation about the origin.
A 270o counterclockwise rotation about the origin is the same effect as a 90o clockwise rotation about the origin.
Rotations by Another Name
A 270o clockwise rotation about the origin is the same effect as a 90o counterclockwise rotation about the origin.
A 270o counterclockwise rotation about the origin is the same effect as a 90o clockwise rotation about the origin.

13. to spin a shape the exact same ROTATION
When some shapes are rotated they create a special situation called rotational symmetry.
to spin a shape
the exact same
When some shapes are rotated they create a special situation called rotational symmetry.
Most playing cards have a rotational symmetry of 180o so you don’t have to turn your cards the right way.
Most playing cards have a rotational symmetry of 180o so you don’t have to turn your cards the right way.

14. ROTATIONAL SYMMETRY
A shape has rotational symmetry if, after you rotate 180o or less, 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?
ROTATIONAL SYMMETRY
A shape has rotational symmetry if, after you rotate 180o or less, 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
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.

15. So this shape is said to have rotational symmetry.
A shape has rotational symmetry if, after you rotate one half-turn or less, it is the same as the original shape.
Here is another example…
As this shape is rotated 360, is it ever the same before the shape returns to its original direction?
ROTATIONAL SYMMETRY
A shape has rotational symmetry if, after you rotate one half-turn or less, it is the same as the original shape.
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.
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

16. ROTATIONAL SYMMETRY
A shape has rotational symmetry if, after you rotate one half-turn or less, it is the same as the original shape.
Here is another example…
As this shape is rotated 360, is it ever the same before the shape returns to its original direction?
ROTATIONAL SYMMETRY
A shape has rotational symmetry if, after you rotate one half-turn or less, it is the same as the original shape.
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
No, when it is rotated 360 it is never the same.
So this shape does NOT have rotational symmetry.

17. Does this shape have rotational symmetry?
Yes, when the shape is rotated 60o , 120 and 180o it is the same. Since these are all less than 180, this shape HAS rotational symmetry.
ROTATIONAL SYMMETRY
Does this shape have rotational symmetry?
Yes, when the shape is rotated 60o , 120 and 180o it is the same. Since these are all less than 180, this shape HAS rotational symmetry.

18. Dilation changes the size of the figure without changing the shape.
Dilation changes the size of the shape without changing the shape.
When you enlarge a photograph or use a copy machine to reduce a map, you are making dilations.
When you enlarge a photograph or use a copy machine to reduce a map, you are making dilations.

19. DILATION
An Enlargement means the shape is bigger and the scale factor is greater than 1.
A Reduction means the new shape is smaller and the scale factor is between 0 and 1.
DILATION
An Enlargement means the shape is bigger and the scale factor is greater than 1.
A Reduction means the new shape is smaller and the scale factor is between 0 and 1.
The scale factor tells you by what factor something is enlarged or reduced.
The scale factor tells you by what factor something is enlarged or reduced.

20. DILATION
Notice each time the rabbit transforms the shape stays the same and only the size changes.
DILATION
Notice each time the rabbit transforms the shape stays the same and only the size changes.

21. DILATION Look at the pictures below
Dilate the image with a scale factor of 75%
DILATION
Look at the pictures below
Dilate the image with a scale factor of 75%
Dilate the image with a scale factor of 150%
Dilate the image with a scale factor of 150%

22. Look at the pictures below
DILATION
Look at the pictures below
Dilate the image with a scale factor of 100%
DILATION
Look at the pictures below
Dilate the image with a scale factor of 100%
Why is a dilation of 75% smaller, a dilation of 150% bigger, and a dilation of 100% the same?
Why is a dilation of 75% smaller, a dilation of 150% bigger, and a dilation of 100% the same?

23. The Scale Factor of a Dilation Centered at Point C
If C and P are distinct points, you can find the scale factor of a dilation centered at C by the following equation.
The Scale Factor of a Dilation Centered at Point C
If C and P are distinct points, you can find the scale factor of a dilation centered at C by the following equation.

24. Dilations Centered at the Origin
If a dilation is centered at the origin, which is often the case, you can use the scale factor to easily find the image coordinates. All you have to do is multiply the pre-image coordinates by the scale factor. You can also find the coordinates of the pre-image by dividing the image coordinates by the scale factor. Do remember, this only works for dilations centered at the origin.
Example:
Find the coordinates of the image of
when dilated by a scale factor of 3 centered at the origin.
Dilations Centered at the Origin
If a dilation is centered at the origin, which is often the case, you can use the scale factor to easily find the image coordinates. All you have to do is multiply the pre-image coordinates by the scale factor. You can also find the coordinates of the pre-image by dividing the image coordinates by the scale factor. Do remember, this only works for dilations centered at the origin.
Example:
Find the coordinates of the image of
when dilated by a scale factor of 3 centered at the origin.
Solution:
Multiply all x- and y-coordinates by 3.
Solution:
Multiply all x- and y-coordinates by 3.

25. Summary This book is being rotated and dilated!
Rotations and dilations are transformations. Rotations do not change the size or shape of a figure, they simply turn them about a fixed point. Dilations do change the size of a figure but not the shape. There are rules that make it easier to find image points of both of these transformations when they are centered at the origin.
This book is being rotated and dilated!
Summary Rotations and dilations are transformations. Rotations do not change the size or shape of a figure, they simply turn them about a fixed point. Dilations do change the size of a figure but not the shape. There are rules that make it easier to find image points of both of these transformations when they are centered at the origin.
This book is being rotated and dilated!