Recap of Rigid Transformations

Recap of Rigid Transformations

by Ms. Smith

​Transformations

​A transformation takes a figure and changes it by moving it in the coordinate plane. There are four types of transformations: reflections, rotations, translations, and dilations.

​

Three of the transformations are called "rigid transformations".  This means that the figure will be congruent to the original.  Unlike rigid transformations, dilations affect the size of the figure and create images that are similar.

Multiple Choice

Which transformation results in an image than has a different size than the pre-image?

• Translation

• Reflection

• Rotation

• Dilation

​New or Old

​pre-image: the original

​image: the result after a transformation

• ​we can identify the image because it will be labeled with the prime symbol ( ' )

Multiple Select

Which of the following represents a pre-image?

• $$\Delta ABC$$  

• $$\Delta A'B'C'$$  

• $$\Delta L'A'P$$  

• $$\Delta DES$$  

​TranSLations--SLide

​Definition-

• ​translation: you slide a figure from one position to another without turning it.

​

​Characteristics:

• ​Creates a CONGRUENT image (same size)

• ​Does NOT change orientation (direction it faces)

​Which way do we go?

​translations are often written in arrow notation

​

​for x value (horizontal movement):

• if we ADD to x, we move RIGHT

• ​if we SUBTRACT from x, we move LEFT

​

​for y value (vertical movement)

• ​if we ADD to y, we move UP

• ​if we SUBTRACT from y, we move DOWN

Multiple Choice

Translations create images that are congruent to the pre-image.

• TRUE

• FALSE

Multiple Choice

Translations will change the direction (orientation) of a pre-image.

• TRUE

• FALSE

Multiple Choice

Describe the translation performed in the picture.

• 5 units left,

  1 unit down

• 1 unit left,

  5 units down

• 5 units right,

  1 unit up

• 1 unit right,

  5 units up

Multiple Choice

Describe the transformation in the picture.

• (x + 3, y + 5)

• (x + 5, y + 3)

• (x - 5, y - 3)

• (x - 3, y -5)

​ReFLections - FLip

Definition: flips an object over a line to create a mirror image

​

​Characteristics:

• ​Creates an image that is CONGRUENT (same size)

• ​Changes orientation (direction) of pre-image

​Which way do we go?

​We will focus on reflecting over 3 lines:

​x-axis

​y-axis

​y=x

​When reflecting over:

​x-axis: you keep the x value and change the sign of the y value

​y-axis: you keep the y value and change the sign of the x value

​y=x: you switch the places of the x and y value but keep their signs the same

Multiple Choice

Which line is this pre-image reflected over?

• x-axis

• y-axis

• line y=x

Multiple Choice

What would be the coordinates of A' if $$\Delta ABC$$  is reflected over the x-axis?

• (0, 4)

• (0, -4)

• (-4, 0)

• (4, 0)

Multiple Choice

What would be the coordinates of C if we reflected the  $$\Delta$$  over the x-axis then over the y-axis?

• (4, -1)

• (-1,4)

• (-4, 1)

• (4, 1)

​RoTAtion - Turn Around

​Definition: turns an object around a point

​

​Characteristics:

• ​Creates CONGRUENT image (same size)

• ​Changes orientation (direction)

​Which way do we go?

​For rotations we need to know which direction and how many degrees we are going.

​* If you are going you flip the order of the numbers and give them the sign of the quadrant they are in.

​*If you are going either direction, you are going to

keep the order but change the signs of

both x and y values.​

Multiple Choice

Which direction was  $$\Delta DEF$$  rotated?

• 180 clockwise

• 90 counterclockwise

• $$270\degree$$  right

• up 3 units

  left 5 units

Multiple Choice

If we rotate $$\Delta ABC\ 90\degree$$  ccw what will be the new coordinates of B?

• (4, 4)

• (4,-4)

• (-4, 4)

• (-4, -4)

Multiple Choice

How many degrees and what direction was the pre-image rotated. 

• $$180\degree$$  

• $$270\degree\ ccw$$  

• $$90\degree\ clockwise$$  

• $$90\degree\ ccw$$  

Poll

Which (if any) of the transformations are you still in need of more help with?

• Translations

• Reflections

• Rotations

• None of them

• All of them