translation & reflection
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Form 2 : Chapter 11
Transformations
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Identify a Translation
All points move same distance and in the same
direction.
Translation
NOT Translation
NOT Translation
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Identify a Translation
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
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Identify a Translation
The values ofa and b can be positive or negativeaccording to the direction of movement.
a negative a positiveb negative
b positiveab
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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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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
Move 2 units
to the right
O
Translation means
move the object 2 units
to the right and 3 units
downward.
23
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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
K
Move 2 units
to the right
Move 3 units
down
O
Translation means
move the object 2 units
to the right and 3 units
downward.
23
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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.
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Describe the translation that maps objectR
to imageR.
R
R
FigureR is mapped tofigureR undertranslation .3
4
+3
-4
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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
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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.
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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
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x
2 4
y
2
1
O
1
2
3
4
2
Find the coordinates of the image of point P
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
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x
2 4
y
2
1
O
1
2
3
4
2
Find the coordinates of the image of point P
under a reflection in they-axis.
P
P
axis of reflection
4
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x
2 4
y
2
1
O
1
2
3
4
2
Find the coordinates of the image of point P
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
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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
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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
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