translation & reflection

7/29/2019 Translation & Reflection

1/17

Form 2 : Chapter 11

Transformations


2/17

Identify a Translation

All points move same distance and in the same

direction.

Translation

NOT Translation

NOT Translation


3/17


Translation is described

(a) by stating the direction using horizontal (left or

right) movement followed by vertical (up or

down) movement,

(b) in the form , where a represents horizontal

movement and b represents vertical movement.

a

b


4/17


The values ofa and b can be positive or negativeaccording to the direction of movement.

a negative a positiveb negative

b positiveab


5/17

The image coordinates of the point K(1,4)

under the translation is2

3

x

y

1 2 3 4

1

2

3

4

5

6

K

O

Translation means

move the object 2 units

to the right and 3 units

downward.

23


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3

x

y

1 2 3 4

1

2

3

4

5

6

K

Move 2 units

to the right

O

Translation means



downward.

23


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3

x

y

1 2 3 4

1

2

3

4

5

6

K

K

Move 2 units

to the right

Move 3 units

down

O

Translation means



downward.

23


8/17

Describe the translation that maps objectR

to imageR.

R

R

Step 1: Choose a vertex

on figureR.Step 2: Move 3 units to the

right and 4 units

down to reach the

corresponding

point in figureR.


9/17

Describe the translation that maps objectR

to imageR.

R

R

FigureR is mapped tofigureR undertranslation .3

4

+3

-4


10/17

Identify a Reflection

Reflection is a transformation where all the points

on a plane are reflected in a line called the axis of

reflection.

axis of reflection

object


11/17

Identify a Reflection

Reflection is a transformation where all the points

on a plane are reflected in a line called the axis of

reflection.axis of reflection

object image

Every point of an object

and the corresponding

points of its image

have the sameperpendicular distance

to the axis of reflection.


12/17

1

Ox

2 4

y

2

1

2

3 P

4

2

Find the coordinates of the image of point P

under a reflection in thex-axis.

axis of reflection


13/17

x

2 4

y

2

1

O

1

2

3

4

2


under a reflection in thex-axis.

P is 2 units abovex-axis.

So,P is 2 units below

x-axis.

P

P ThereforeP is (4, 2).

2

2


14/17

x

2 4

y

2

1

O

1

2

3

4

2


under a reflection in they-axis.

P

P

axis of reflection

4


15/17

x

2 4

y

2

1

O

1

2

3

4

2


under a reflection in they-axis.

P is 4 units to the rightofy-axis.

So,P is 4 units to the

left ofy-axis.

P

P

ThereforeP is (4, 2).

axis of reflection

44


16/17

Find the axis of reflection for the given

object and its image.

Step 1: JoinA toA(or any

point to its image).Step 2: Construct a

perpendicular

bisector to the

lineAA. Label it

PQ. (find

midpoint and

use 90

o

)

C

B

B

A

A

C

Q

P


17/17

Find the axis of reflection for the given

object and its image.

The perpendicular bisector

PQ is the axis of reflection.

C

B

B

A

A

C

Q

P

translation & reflection

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