Translations

​Standard: MGSE8.G.2

Understand that a two‐dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

​Learning Targets

1. I can explain whether or not two figures are congruent using transformations.

2. I can explain the series of transformations used to transform a figure to its congruent conterpart.

​Essential Vocabulary

1. Transformations

2. Translations

3. Rotation

4. Reflection

5. X-Axis

6. Y-Axis

​Essential Vocabulary

​6. Congruent

7.​ Similar

8.​ Pre-Image​

9.​​ Image

10.C​oordinates

11​. Line of Reflection

​Essential Question

​1. What is the relationship between reflections, translations, and rotations?

​

Multiple Choice

Are these triangles similar?

• Yes

• No

​Vocabulary

• Transformation - an operation that maps an original figure onto a new figure ​

• Original Figure - is called the PRE-IMAGE

• New Figure - is called the IMAGE​

• Rigid Transformation - a transformation that creates an image that is congruent to the pre-image. (translation, reflection, and rotation ONLY)​

THESE ARE THE ONLY 3 TRANSFORMATIONS THAT CREATE CONGRUENT IMAGES! RIGID TRANSFORMATIONS

​Types of Transformations

​Translation - a slide that moves all points in the same direction and same distance

​Reflection - a FLIP over a certain line, all points from the pre-image to image are the same distance apart.

​Rotation - a TURN around a fixed point, all points from the pre-image to image are the same distance apart.

THESE ARE THE ONLY 3 TRANSFORMATIONS THAT CREATE CONGRUENT IMAGES! RIGID TRANSFORMATIONS

​Types of Transformations

​Translation - a slide that moves all points in the same direction and same distance

​Reflection - a FLIP over a certain line, all points from the pre-image to image are the same distance apart.

​Rotation - a TURN around a fixed point, all points from the pre-image to image are the same distance apart.

Multiple Choice

Fill in the blank: Translations create __________ figures.

• Similar
• Congruent

Multiple Choice

Fill in the blank: Rotations create __________ figures.

• Similar
• Congruent

Multiple Choice

Fill in the blank: Reflections create __________ figures.

• Similar
• Congruent

Multiple Choice

Name the transformation.

• Translation
• Reflection
• Rotation

Multiple Choice

What is this picture an example of? 

• An angle
• A cat vertex 
• Rotation 

Multiple Choice

What transformation is happening to the red triangle to get to the blue triangle?

• Translation
• Rotation
• Reflection

Open Ended

What does it mean to transform something?

Open Ended

Today, we're focusing on translations. Have you heard this word before? What does it mean to you? (can be math related or not)

Translations

• Are a type of transformation that move a shape (by shifting or sliding) to another location

• Can move an image left, right, up, or down

• The pre-image is the original image and the image is the image after it has been transformed
  

• Make note of the notation used for the pre-image and image

Open Ended

What else did you notice about the pre-image and image? What do you wonder?

How do we "perform" transformations in the coordinate plane?

Open Ended

What are some differences in the two methods for performing translations discussed in the video?

Multiple Choice

Point Q is located at (4, 5). We want to shift it 6 units right. What would be the location of point Q'?

• (10, 5)

• (5, 10)

• (4, 11)

• (11, 4)

• I'm not sure, I need more explanation.

Multiple Choice

Point K is located at (-2, 0). We want to shift it down 3 units. What would be the location of point Q'?

• (-5, 0)

• (0, -3)

• (-2, -3)

• (-5, -3)

• I'm not sure, I need more explanation.

Poll

On the graph shown, the point R' was created by moving point R _____________.

• 6 units left

• 6 units right

• 4 units up

• 4 units down

Mapping Notation

Instead of writing x units left/right and y units up/down, we can use mapping notation. The number being added or subtracting to each coordinate let's you know how many units to move AND in what direction.

Subscript Notation

• The capital T is used to denote a translation

• The numbers in parenthesis DO NOT represent ordered pairs

• The numbers in parenthesis are directions; they let you know which way to move on the coordinate plane

• In this example, the notation is telling use to move point A left 1 unit and up 2 units to create point A' at (2, 4)

• This notation is helpful if you don't have a coordinate plane to look at

Open Ended

What is the meaning of the notation in relation to translations? 

$$\left(x,\ y\right)\rightarrow\ \left(x-3,\ y+6\right)$$  

Multiple Choice

Which notation denotes a translation of a pre-image 5 units right and 2 units down?

• $$T_{\left(-5,\ 2\right)}$$

• $$T_{\left(-2,5\right)}$$

• $$T_{\left(5,-2\right)}$$

• $$T_{\left(-2,\ -5\right)}$$

Open Ended

Triangle A'B'C' has the coordinates A: (8, 8) B: (8, 4) C: (5, 4) The mapping notation

$$\left(-3,\ 9\right)$$  was used to create this image. What are the coordinate of point A in the pre-image?

Open Ended

Summarize:

1) What is your definition of translations?

2) How do the notations help with performing translations in the coordinate plane?

Poll

Choose the topics you still need help understanding. (You can choose more than 1)

• None. I understand everything in today's lesson.

• Performing translations using mapping notation

• Performing translations using subscript notation

• The definition of a translation.

• The difference between image and pre-image.