Solutions to the Symmetry WS 1. a 2. b 3. a 4. c 5. a 6. c 7. b 8. a 9. c 10. a SIDE 1 1. yes 2. 2 3. 8 4. 4 5. No 6. 4 SIDE 2

Solutions to the Symmetry WS

1. a2. b3. a4. c5. a

6. c7. b8. a9. c10. a

SIDE 1

1. yes2. 23. 84. 45. No6. 4

SIDE 2

We are learning to…identify and translate images on a coordinate plane.

Translations (Slide)

Homework: WS – Translations in the Coordinate Plane

Translations on the Coordinate Plane

Translations on theCoordinate Plane

In chess, there are rules governing how many spaces and in what direction each game piece can be moved

The diagram below shows the legal moves of the piece known as the knight

A translation is a rigid isometry.Isometry – transformation that maintains size and shape.

The original object (preimage) and its translation (image) have the

same shape and size, and they face in the same direction.

A translation is a transformation of the plane that slides every point of a figure the same

distance in the same direction.

preimage

image

3. Notation:

This may also be seen as T-7,-3( x, y) = (x -7, y - 3).

There are several ways to indicate that a translation is to occur:

1. Description (verbal):7 units to the left and 3 units down.

2. Mapping: (x, y) (x -7, y – 3)

In this example: each of these sets of directions indicated that you are to move each point in the preimage 7 units left then 3 units down.

Example: the "slide" (translation) moves the figure7 units to the left and 3 units down.

𝑇 (−7 ,−3 ) (𝑥 , 𝑦 )=(𝑥−7 , 𝑦−3)

Quad ABCD is the preimageQuad A’B’C’D’ is the image

A (2,4) A’ (-5,1)B (4,4) B’ (-3,1)C (5,2) C’ (-2,-1) D (2,1) D’ (-5,-2)

Use the given rule to translate the figure. Then describe the transformation.

(1,3)

(1,1)

(4,1)

Rule: (x, y+3)

Add 3 to the y’s.

Preimage Image(1, 6)

(1, 4)

(4, 4) translated figure up 3 units

preimage

image


(-3,-2)

(-3,-4)

(0,-4)

Rule: (x-2, y)

Subtract 2 from x’s

Preimage Image(-5, -2)

(-5, -4)

(-2, -4)translated figure left 2 units

preimage

image

Summary of Translations

Add to x Translates RIGHT

Subtract from x Translates LEFT

Add to y Translates UP

Subtract from y Translates DOWN

Translations in the Coordinate Plane:In the example below, notice how each vertex moves the same distance in the same direction.

𝑇 (6 , 0) (𝑥 , 𝑦 )=(𝑥+6 , 𝑦 )Translation notation

preimageimage

Explain how to translate an image with the following directions:

Translation Mapping

How should we translate this object?

(x + 4, y + 2)

(x – 6, y + 15)

(x + 12, y – 5)

(x – 8, y – 10)

Slide the figure 4 units right, and 2 units up.

Slide the figure 6 units left, and 15 units up.

Slide the figure 12 units right, and 5 units down.

Slide the figure 8 units left, and 10 units down.

Write the following in translation notation:

Translation DirectionsTranslation

NotationMapping

“Translate a figure right 4 and up 5.”

“Translate a figure left 9 and up 6.”

“Translate a figure left 10 and down 13.”

“Translate a figure right 2 and down 3.”

(x + 4, y + 5)

(x - 9, y + 6)

(x - 10, y – 13)

(x + 2, y – 3)

5,4T

6,9T

13,10 T

3,2 T

Translate the figure using the following directions: (x + 3, y – 7).

D

B

A

C

D ′

B ′

A′

C ′

Find the coordinates of the translated image:

A′:___________________

B′:___________________

C′:___________________

D′:___________________

(1, 1)

(-4, -4)

(6, -1)

(5, -6)

Translate the figure using the following directions:

B

A

B ′C ′

Find the coordinates of the translated image:

A′:___________________

B′:___________________

C′:___________________

(-4, 4)

(0, -3)

(4, 5)

C

A ′

http://www.virtualnerd.com/middle-math/integers-coordinate-plane/transformations

http://www.misterteacher.com/alphabetgeometry/transformations.html#Slide

http://www.teachertube.com/viewVideo.php?video_id=172666

http://www.teachbuzz.com/lessons/transformations-coordinate-plane



http://www.misterteacher.com/alphabetgeometry/transformations.html






Write the coordinate of the vertices of the image.

The coordinates of the vertices of quadrilateral A'B'C'D' are A'(–3, 1), B'(0, 2), C'(0, –1), and D'(–3, –3).

Quadrilateral ABCD (x – 4, y – 2) A’B’C’D’

A(1, 3) (1 – 4, 3 – 2) A’(–3, 1)

B(4, 4) (4 – 4, 4 – 2) B’(0, 2)

C(4, 1) (4 – 4, 1 – 2) C’(0, –1)

D(1, –1) (1 – 4, –1 – 2) D’(–3, –3)


(1,3)

(1,1)

(4,1)

Rule: (x, y+3)

Add 3 to the y’s.


(1, 4)

(4, 4)translated figure up 3 units

(-4,3)

(-4,1)

(-1,1)

Rule: (x+5, y)

Add 5 to the x’s.


(1, 1)

(4, 1)translated figure right 5 units


Describe each transformation.

(x+10, y)

(x–5, y)

(x, y+7)

(x, y–6)

(x+3,y–7)

(x–4,y–5)

(x–8,y+9)

translates right 10

translates left 5

translates up 7

translates down 6

translates right 3 and down 7

translates left 4 and down 5

translates left 8 and up 9


http://www.misterteacher.com/alphabetgeometry/transformations.html#Slide








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Solutions to the Symmetry WS 1. a 2. b 3. a 4. c 5. a 6. c 7. b 8. a 9. c 10. a SIDE 1 1. yes 2. 2 3. 8 4. 4 5. No 6. 4 SIDE 2