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GEOMETRY�

TERM 2

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Table of Contents

Page #	Title	UNIT

# Translations & Reflections GS

#

Translations & Reflections

GS

DO IT NOW

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MEASUREMENT

Represent transformations using the Cartesian coordinate plane, and make connections between transformations and the real world

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CURRICULUM

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By the end of this lesson…

Identify and draw translations
Identify and draw reflections

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CARTESIAN PLANE

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ONE OF THE MOST IMPORTANT THINGS TO LEARN FOR HIGHSCHOOL!

CARTESIAN PLANE

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CARTESIAN

PLANE

QUADRANT

1

QUADRANT

2

QUADRANT

3

QUADRANT

4

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Which quadrant �is it in?

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CARTESIAN

PLANE

QUADRANT

1

QUADRANT

2

QUADRANT

3

QUADRANT

4

The “x” axis

The “y” axis

Q R S T U V W X Y Z

REMEMBER: THE “X” COMES FIRST!

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CARTESIAN

PLANE

QUADRANT

1

QUADRANT

2

QUADRANT

3

QUADRANT

4

MRSTAV

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CARTESIAN

PLANE

QUADRANT

1

QUADRANT

2

QUADRANT

3

QUADRANT

4

MRSTAV

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CARTESIAN

PLANE

QUADRANT

1

QUADRANT

2

QUADRANT

3

QUADRANT

4

Is there a quadrant that both the X and the Y are negative?

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CARTESIAN

PLANE

QUADRANT

1

QUADRANT

2

QUADRANT

3

QUADRANT

4

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PLOTTING A POINT ON A CARTESIAN PLANE

(6,4)

x y

6

Start at ZERO
Move the number of the x

Make sure you go in the right direction

From that point, move the number of the y
Plot your point

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PLOTTING A POINT ON A CARTESIAN PLANE

(-6,-4)

x y

(6,4)

Start at ZERO
Move the number of the x

Make sure you go in the right direction

From that point, move the number of the y
Plot your point

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READING A POINT ON A CARTESIAN PLANE

(__ ,__)

x y

(6,4)

(-6,-4)

5

-3

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READING A POINT ON A CARTESIAN PLANE

x y

(6,4)

(-6,-4)

(5,-3)

(__ ,__)

7

-

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WORD WALL

TRANSFORMATION – a change in the position, size, or shape of a figure
PREIMAGE – the original figure
IMAGE – the figure after the transformation
PRIME - We use primes (‘) to label the image.
ISOMETRY – a transformation that only changes the position of the figure

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How can point A shift to its A' image by moving only horizontally and vertically.�

WORD WALL

PRE-IMAGE

A

A’

IMAGE

PRIME

A’’

DOUBLE PRIME

A’’’

TRIPLE PRIME

IMAGE

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TRANSLATE

“TRANSLATION”

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A

A’

4 units right

7 units down

Image A’ is translated 4 units right,

and 7 units down from Preimage A.

THEREFORE:

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TRY ME

5

-

+

4

L’

( ___ , ___ )

= -1 + 5

4

= 6 - 4

2

UP = (+)

DOWN = (-)

LEFT = (-)

RIGHT = (+)

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TRY IT

5

-

+

4

L’

( ___ , ___ )

= -1 + 5

4

= 6 - 4

2

UP = (+)

DOWN = (-)

LEFT = (-)

RIGHT = (+)

2

+

-

5

R’

( ___ , ___ )

= 0 - 2

-2

= 8 + 5

13

Y’

( ___ , ___ )

7

-6

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< >

2

-

4

2

-

+

4

< >

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Find multiple solutions

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A

A’

4 units right

7 units down

Image A’ is translated 4 units right,

and 7 units down from Preimage A.

THEREFORE:

< , >

4

-7

OR:

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TRY IT

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TRY IT

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How can point A shift to its A' image by moving only horizontally and vertically.�

ACCOUNTABLE TALK

translation
ordered pairs
horizontal
Vertical
positive
negative
Quadrant (1, 2, 3 & 4)

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WHEN WILL MY REFLECTION SHOW

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REFLECTION

“REFLECT”

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5

10

-5

-10

-5

-10

-15

15

10

5

S(-5, 8)

S

S’

REFLECT OVER THE Y AXIS

EQUAL DISTANCE ON BOTH SIDES OF THE MIRROR

S’(5, 8)

“REFLECT”

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5

10

-5

-10

-5

-10

-15

15

10

5

E

REFLECT OVER THE Y AXIS

EQUAL DISTANCE ON BOTH SIDES OF THE MIRROR

J

R

J’

R’

J(-4, 4)

R(-14, -5)

E(-2, 3)

E’

J(4, 4)

R(14, -5)

E’(2, 3)

“REFLECT”

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5

10

-5

-10

-5

-10

-15

15

10

5

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5

10

-5

-10

-5

-10

-15

15

10

5

REFLECT OVER THE X AXIS

EQUAL DISTANCE ON BOTH SIDES OF THE MIRROR

“REFLECT”

N (10, 4)

A (14, 8)

Z (15, 3)

Z’(15, -3)

N’(10, -4)

A’(14,-8)

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5

10

-5

-10

-5

-10

-15

15

10

5

REFLECT OVER THE X AXIS

EQUAL DISTANCE ON BOTH SIDES OF THE MIRROR

“REFLECT”

N (10, 4)

A (14, 8)

Z (15, 3)

Z’(15, -3)

N’(10, -4)

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5

10

-5

-10

-5

-10

-15

5

“REFLECT”

REFLECT OVER y = 2

EQUAL DISTANCE ON BOTH SIDES OF THE MIRROR

B (-9, 6)

O (-5, 10)

R (-4, 5)

R’(-4, -1)

B’(-9, -2)

O’(-5,-7)

(0, 2)

TRY IT:

REFLECT △BRO OVER y = 2

REFLECT △B’R’O’ OVER x = 4

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5

10

-5

-10

-5

-10

-15

5

“REFLECT”

15

10

REFLECT OVER THE X AXIS

EQUAL DISTANCE ON BOTH SIDES OF THE MIRROR

N (10, 4)

A (14, 8)

Z (15, 3)

Z’(15, -3)

N’(10, -4)

A’(14,-8)

REFLECT OVER y = 2

EQUAL DISTANCE ON BOTH SIDES OF THE MIRROR

B (-9, 6)

O (-5, 10)

R (-4, 5)

R’(-4, -1)

B’(-9, -2)

O’(-5,-7)

(0, 2)

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5

10

-5

-10

-5

-10

-15

5

“REFLECT”

REFLECT OVER y = 2

EQUAL DISTANCE ON BOTH SIDES OF THE MIRROR

B (-9, 6)

O (-5, 10)

R (-4, 5)

R’(-4, -1)

B’(-9, -2)

O’(-5,-7)

(0, 2)

TRY IT:

REFLECT △BRO’ OVER x = 4

(4, 0)

REFLECT OVER x = 4

△BRO

△BRO’

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5

10

-5

-10

-5

-10

-15

5

“REFLECT”

REFLECT OVER y = 2

EQUAL DISTANCE ON BOTH SIDES OF THE MIRROR

B (-9, 6)

O (-5, 10)

R (-4, 5)

R’(-4, -1)

B’(-9, -2)

O’(-5,-7)

(0, 2)

15

10

TRY IT:

REFLECT △BRO’ OVER x = 4

(4, 0)

REFLECT OVER x = 4

EQUAL DISTANCE ON BOTH SIDES OF THE MIRROR

R’’(12, -1)

B’’(17, -2)

O’’(13,-7)

△BRO

△BRO’

△BRO’’

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A triangle (∆DEF) is reflected on the y-axis.

D(-4,1) and E(-3,-2)

Choose a point F, and find the image after the

reflection.

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A triangle (∆DEF) is reflected on the x-axis.

D(-4,1) and E(-3,-2)

Choose a point F, and find the image after the reflection.

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5

10

-10

-5

-10

-5

5

10

15

-15

0

USE TO MAP

Drag & resize these elements to show your trip

🡨 USE THESE ELEMENTS TO MARK YOUR TRIP

a

b

c

d

e

f

TRANSLATE

CANADA

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INSTRUCTIONS	ORDERED PAIR
Start in ____________, ___	(-3, -6)
Take an Uber < 9, 0 >
Take Air STAV over the y axis
Take a bus < -3, ___ >	( __ , -5)
Fly a jet over y = ____	( -9, 1)
Translate < 4, -2 >
Fly a blimp over x = -8.5
What is your final destination: _______________________________

INSTRUCTIONS	ORDERED PAIR
Start in Vancouver, BC
Translate < 8, 7 >
Reflect over the y axis
Reflect over y = -2
Translate < 2, -1 >
Translate < -2, 5 >
Reflect over x = 10
What is your final destination: _______________________________

INSTRUCTIONS	ORDERED PAIR
Start in Toronto, ON






Create 3 reflections & 3 translations that will end at PEI

INSTRUCTIONS	ORDERED PAIR
Start in Calgary, AB
Reflect over x = -4
Translate < ___ , ___ >	( 0 , -7 )
Reflect over x = ___	(10, -7)
Reflect over y = -4
Translate < -4 , ___ >	(___, -6)
Translate < -12 , 0 >
What is your final destination: _______________________________

INSTRUCTIONS	ORDERED PAIR
Start in Yellowknife, NT
Take STAVexpress < -6,3 >
Translate in a taxi 9 units south
Fly AirSTAV over the x = 0
Fly west over x = 11
Bus 1 unit W & 3 units south
Drive < -1, -1 >
What is your final destination: _______________________________

ROAD TRIP!

Name: ______________________________

Fill in the charts as you explore Canada via STAVexpress (Translations) and AirSTAV (Reflections).

Chart your journey on the �Google Slides assignment on Google Classroom

(#,#)

Type destination here

(#,#)

Type destination here

(#,#)

#

(#,#)

#

(#,#)

Type destination here

location

(#,#)

#

(#,#)

Type destination here

#

Type step 1 here

Type step 2 here

Type step 3 here

Type step 4 here

Type step 5 here

Type step 6 here

#

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5

10

-10

-5

-10

-5

5

10

15

-15

0

USE TO MAP

Drag & resize these elements to show your trip

🡨 USE THESE ELEMENTS TO MARK YOUR TRIP

a

b

c

d

e

f

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