Transformations

​Transformations...

​Translations- SLIDES

​Reflections- FLIPS

​Rotations -TURNS

​pre-image: original shape

​

​image: what is created as a result of the transformation

Multiple Choice

The original figure prior to a transformation.

• Pre-image

• Image

Multiple Choice

What transformation is shown on the graph?

• translation

• reflection across y-axis

• rotation

• reflection across x-axis

Multiple Choice

Identify the transformation from ABC to A'B'C'.

• Reflection across the x-axis

• Reflection across the y-axis

• translation

• rotation

Multiple Choice

What transformation is shown?

• translation

• reflection across the x-axis

• reflection across the y-axis

• rotation

Translations

​Translations

• ​"Slide" of an object

• ​An object can move:

  • ​left/right

  • ​up/down

​Describe the translation.

​1) Decide which is the pre-image

In this case, the pre-imag​e is the shape labeled ABCD. The image is the shape A'B'C'D'.

​

​2) How do you get to the image?

​Start on the pre-image and count to get to the image.

​ 6 units left and 3 unit up

Multiple Choice

Translate the blue shape to the pink shape...

• 5 Right

  2 Down

• 5 Left

  2 Up

• 3 Right

  1 Down

• 3 Left

  1 Up

Multiple Choice

Translate the green shape to the blue shape...

• 3 Left

  3 Down

• 3 Right

  3 Up

• 2 Right

  3 Up

• 2 Left

  3 Down

​Describing with MATH

​We can see that this shape moves:

​

​right 6 units and down 4 units.

​

​So how do we write this with math?

​

​(x+6, y -4)

​Remember...

​x + # will move it to the right

​x - # will move it to the left

​

​y + # will move it up

​y - # will move it down

​

​example: (x + 2, y - 3) this will move right 2 and down 3

​(x - 5, y + 4) this will move 5 left and up 4

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

Write the rule for this translation:

Slide 5 up and 7 right

• (x, y)---->(x + 5, y + 7)

• (x, y)-----> (x + 7, y + 5)

• (x, y)----> (x - 7, y + 5)

Multiple Choice

Identify the transformation from ABC to A'B'C'.

• (x+8, y+4)

• (x-8, y-4)

• (x+4, y+8)

• (x-4, y-8)

Reflections​

​What is a reflection?

​Reflections

​When we reflect, we "flip" the shape.

​

​We can reflect across the x-axis or the y-axis.

​

Multiple Choice

Flipping a figures is a ...

• Rotation

• Reflection

• Dilation

• Translation

Multiple Choice

What axis is the image reflected over?

• X-axis

• Y-axis

Multiple Choice

What axis is the triangle being reflected over?

• X-axis

• Y-axis

Multiple Choice

If the dotted figure is the image, the original figure was reflected over the ...

• x-axis

• y-axis

​When we reflect, we have to pay attention to the new coordinates!

​(3,2) is reflected across the x-axis

​

​When we reflect, we have to pay attention to the new coordinates!

​(-2, 4) is reflected across the y-axis.

Multiple Choice

Reflect Point C over the y-axis:

• (-3, 2)

• (3,2)

• (-2,3)

• (3,0)

Multiple Choice

Reflect (6, -3) over the line x-axis.

• (6, 3)

• (-6, -3)

• (-3, 6)

• (3, -6)

Multiple Choice

Reflect Point C over the y-axis:

• (-3, 2)

• (3,2)

• (-2,3)

• (3,0)

Multiple Choice

Reflect over x-axis. Which point would be at (3, -6)

• A

• B

• C

• H

Rotations​

​What is a rotation?

​Rules for rotations

​Rotations occur in the counterclockwise direction unless otherwise stated.

​

​When we rotate, the object will change quadrants on the coordinate plane.

Multiple Choice

How many degrees was the figure rotated?

• 90 degrees counterclockwise 

• 180 degrees

• 90 degrees clockwise

Multiple Choice

How many degrees was the figure rotated?

• 90 degrees counterclockwise 

• 180 degrees

• 90 degrees clockwise

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

Multiple Choice

How many degrees was the figure rotated?

• 90 degrees counterclockwise 

• 180 degrees

• 270 counterclockwise 

• 90 degrees clockwise

Multiple Choice

What is the angle of rotation for this counterclockwise rotation about the origin?

• 90°

• 180°

• 270°

• 360°

​Rotations

​Let's rotate these points.

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

If you were to rotate ABCD 90° counterclockwise about the origin, what would the coordinate of A' be?

• (-5, 5)

• (-3, 5)

• (-5, 3)

• (-3, 3)

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

• (-7,-8)

• (8,-7)

• (-8,7)

• (8,7)

​Rotating a shape

• ​Identify the points on the pre-image.

• ​Rotate those points according to the given rotation.

• ​Draw the image in the correct location.

Multiple Choice

If you were to rotate ABCD 180°  about the origin, what would the coordinate of A' be?

• (-5, 5)

• (-3, -5)

• (-5, 3)

• (-3, 3)