Translations and Rotations

Transformations - Translations and Rotations

Learning Target: I can identify and locate the images of translated and rotated

figures.

Transformation

A change in the position, size, or shape of a geometric figure.

Types of Transformations
● Translations
● Reflections
● Rotations
● Dilations

​Translation

A transformation that maps all of the points of a figure the same direction and the same distance. 

Rotation​

A transformation that changes the orientation of a geometric figure.

Multiple Choice

The new figure created from a transformation is...

• Image

• Pre-image

Multiple Choice

The original figure before a transformation is called the...

• Image

• Pre-image

Multiple Choice

Translations, reflections and rotations are all known as ________________________.

• Geometry

• Transformations

• Congruent

• Similar

Multiple Choice

A slide is also called a _________.

• Translation

• Reflection

• Rotation

• Transformation

Multiple Choice

A turn is also called a ___________.

• Translation

• Reflection

• Rotation

• Transformation

Multiple Choice

How is trapezoid ABCD translated to trapezoid A'B'C'D'?

• Translated 5 units down and 5 units to the right

• Translated 5 units down and 1 to the right

• Translated 8 units down and 5 units to the right

• Translated 5 units down and 8 units to the right

Multiple Choice

What type of transformation is shown?

• Rotation

• Translation

• Reflection

Multiple Choice

Determine where X' would be if you translated X 3 units to the left and 9 units down.

• (-4, 4)

• (-10, 2)

• (-4, -5)

• (-1, 5)

Multiple Choice

What transformation is happening?
(x, y) ----> (x + 2, y - 3) 

• slide up 2, left 3

• slide right 2, up 3

• slide right 2, down 3

• slide left 3, right 2

Multiple Choice

Where would A' be if you translated A 3 units to the right and 4 units down?

• (-4, 4)

• (-1, 0)

• (0, -1)

R90 CW = (x,y) → (y, -x)

From the coordinate (x,y), rotate
the preimage clockwise 90
degrees about the origin.

(-1,4) → (4, 1)

(1,-3) → (-3,-1)

(-4,-2) → (-2, 4)

Multiple Choice

Triangle A is rotated 90° clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A

• B

• C

• D

Multiple Choice

Triangle B is rotated 90° clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A

• B

• C

• D

R180 CW = (x,y) → (-x, -y)

From the coordinate (x,y), rotate
the preimage clockwise 180
degrees about the origin.

(-1,4) → (1, -4)

(1,-3) → (-1, 3)

(-4,-2) → (4, 2)

Multiple Choice

Triangle B is rotated 180° clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A

• B

• C

• D

Multiple Choice

Triangle C is rotated 180° clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A

• B

• C

• D

R270 CW = (x,y) → (-y, x)

From the coordinate (x,y), rotate
the preimage clockwise 180
degrees about the origin.

(-1,4) → (-4, -1)

(1,-3) → (3, 1)

(-4,-2) → (2, -4)

Multiple Choice

Triangle A is rotated 270° counterclockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A

• B

• C

• D

Multiple Choice

Triangle C is rotated 270° counterclockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A

• B

• C

• D

Multiple Choice

Triangle B is rotated 90° counterclockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A

• B

• C

• D

Multiple Choice

Rotate the point (-3,-4) around the origin 180 degrees. State the image of the point.

• (-4,-3)

• (-4,3)

• (4,-3)

• (3,4)

Multiple Choice

Triangle A is rotated 270° counterclockwise with the origin as the center of rotation to create a new figure. Which rule describes rotating 270° counterclockwise?

• (x,y)→(y, -x) 

• (x,y)→(x,y)

• (x,y)→(-y,x)

• (x,y)→(-x,-y)

Multiple Choice

Triangle C is rotated 180° clockwise with the origin as the center of rotation to create a new figure. Which rule describes rotating 180° clockwise?

• (x,y)→(y, -x) 

• (x,y)→(-x,-y)

• (x,y)→(x,y)

• (x,y)→(-y,x)

Multiple Choice

Triangle B is rotated 90° counterclockwise with the origin as the center of rotation to create a new figure. Which rule describes this transformation?

• (x,y)→(y, -x) 

• (x,y)→(x,y)

• (x,y)→(-x,-y)

• (x,y)→(-y,x)

Multiple Choice

Rotate the point (7,8) around the origin 90 degrees counterclockwise.
State the image of the point.

• (-7,-8)

• (8,-7)

• (-8,7)

• (8,7)

Multiple Choice

Rotate the point (-5,8) around the origin 270 degrees counterclockwise. State the image of the point.

• (-8,5)

• (8,-5)

• (8,5)

• (5,-8)

Multiple Choice

Rotate the point (3,3) around the origin 180 degrees counterclockwise. State the image of the point.

• (3,-3)

• (3,3)

• (-3,3)

• (-3,-3)

Multiple Choice

If you rotate point A(-3,4) 180 degrees clockwise and then rotate it again 90 degrees counter clockwise what would be the coordinates of A"?

• (-3,-4)

• (-4,-3)

• (3,-4)

• (4,3)

Multiple Choice

Rotate the point (-3,-4) around the origin 180 degrees. State the image of the point.

• (-4,-3)

• (-4,3)

• (4,-3)

• (3,4)

Rotate Figure ABC R90 CW

R90 CW = (x,y) → (y, -x)

A (-4,2) → A’ ( 2 , 4 )

B (0,3) → B’ ( 3 , 0 )

C (-1, 1) → C’ ( 1 , 1 )

Rotate Figure ABC R180 CCW

R180 CCW = (x,y) → (-x, -y)

A (-4,2) → A’ ( 4 , -2 )

B (0,3) → B’ ( 0 , -3 )

C (-1, 1) → C’ ( 1 , -1 )

Multiple Choice

How many degrees was the figure rotated?

• 90 degrees counterclockwise 

• 180 degrees

• 270 counterclockwise 

• 90 degrees clockwise

Multiple Choice

When you rotate 180 degrees the ( x , y ) becomes ?

• ( y , x )

• ( -y , x )

• ( -x , y )

• ( -x , -y )

Multiple Choice

Identify the transformation from A to D.

• 90^o Clockwise Rotation

• 180^o Rotation

• 270^o  clockwise Rotation

• 360^o Rotation

Multiple Choice

Identify the transformation from B to D.

• 90^o Clockwise Rotation

• 180^o Rotation

• 270^o clockwise Rotation

• 360^o Rotation

Multiple Choice

How many degrees was the figure rotated?

• 90 degrees counterclockwise 

• 180 degrees

• 90 degrees clockwise

Poll

How well do you understand Rotations? (1-5)

1 (I don't understand at all)

-

5 (I got this down)

• 1

• 2

• 3

• 4

• 5