Translations

Translations & Reflections

Poll

Are you excited for summer break?

• Yes!

• No!

• I rather stay at school and do math!

Poll

How do you feel about performing translations?

• I'm a pro!

• I'm okay!

• I need more practice..

• I'm super lost...

Poll

How do you feel about performing reflections?

• I'm a pro!

• I'm okay!

• I need more practice..

• I'm super lost...

Poll

How do you feel about performing rotations?

• I'm a pro!

• I'm okay!

• I need more practice..

• I'm super lost...

Learning Target

• I can determine rules for translations on the coordinate plane.

Translations

• Identify the pre-image and the image.

• Point A is located at (-2, 3)

• Point A' is located at (4, 1)

• Point A was translated 6 units to the right and 2 units down.

• ( x + 6, y - 2)

Translations

• Determine the rule for translating the rectangle.

• Figure moved left 2 units, and down 4 units

• The rule will be ( x - 2, y - 4)

Translations

• Translations involve addition and subtraction

• Adding to the x-axis moves figures to the right, whereas subtracting will move figures left.

• Adding to the y-axis moves figures up, while subtracting will move figures down.

Translations

• Determine A' when the figure is translated 3 units right, and 2 units up.

• Use the grid to determine the new location.

• Or use the algebraic rule to determine the new rule.

• Point A (5, 5) - count the units or use the rule ( x + 3, y + 2)

• Point A' ( 8, 7 )

Translations

slide a figure on the coordinate plane.

Multiple Choice

When I translate a shape, I move only one point.

• TRUE

• FALSE

The original figure is called "pre-image"

Multiple Choice

How many units to the right do I need translate for Figure 1 to be on top of Figure 2?

• 1 unit

• 10 units

• 5 units

• 4 units

Transformed figure is called "image"

Congruent:

Same shape

Same size

When translated, pre-image and image are congruent.

When translated pre-image and image face the same direction.

In the graph, each point on the blue shape is translated 8 units to the right, and 3 units down.

Translations move

• to the left or to the right (horizontal) x

• up or down (vertical) y

Multiple Choice

Which translation best describes the movement from Triangle A and Triangle A'?

• 2 units right and 2 units down

• 2 units left and 2 units up

• 4 units right and 2 units down

• 2 left and 2 down

Multiple Choice

What is congruent?

• Same shape, same size

• Same shape, same color

• Same shape, same height

• Similar shape, same size.

Multiple Choice

After we translate triangle A to triangle A', do the sides stay the same length?

• YES!

• NO!

Multiple Choice

Which translation best describes the movement from Trapezoid A and Trapezoid A'?

• 6 units right and 3 units down

• 3 units left and 6 units up

• 2 units left 4 units up

• 6 units left and 3 units up

Multiple Choice

After translating, which is equal to side AB?

• B'C'

• A'B'

• A'D'

• D'C'

Multiple Choice

When I reflect a shape, does the shape stay the same size?

• NO

• YES

Multiple Choice

Which graph best describes a shape that is reflected over the x - axis?

Multiple Choice

Which graph best describes a shape that is reflected over the x - axis?

Multiple Select

Which graphs best describes a shape that is reflected over the y - axis?

Multiple Choice

FINAL: Which transformations do I need to get from Triangle A to Triangle C?

• Reflect over the x axis THEN reflect over the y axis.

• Translate to the left, THEN reflect over the x axis

• Reflect over the y axis, THEN translate down

• Reflect over the y axis THEN over the x axis

Multiple Choice

Determine the rule that translated the figure.

• ( x + 4, y - 3)

• ( x - 3, y + 4)

• ( x - 1, y + 0)

• ( x - 4, y - 4)

​Review

Translations: Moving a shape left, right, down, or up a certain amount of units.

​

Reflections: Mirroring a shape across a line of reflection.​

Poll

The video mentioned shapes being flipped, turned around, and shifted.

Which of those descriptions best fit or describe a rotation?

• flipped

• turned around

• shifted

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?