2 TRANSLATION_use this - Copy

G15 Translation

Translation

When an object is moved in a straight line in a given
direction we say that it has been translated.

As an example, we can translate triangle ABC 5 units to the

right and 2 units upward: A’

image

object A B’
C’

CB

Every point in the shape moves the same distance in the
same direction.

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Determining translations

Which shows a translation? Justify.
1) 2)

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Determining translations

Which shows a translation? Justify.
3) 4)

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Describing translations

Translation can be described using 2
methods:
(1) By stating the DIRECTION &

DISTANCE of the movement

(2) By VECTOR form

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Describing translations

Method 1: By stating the DIRECTION & DISTANCE of the
movement

When we describe a translation we always
give the movement left or right first followed
by the movement up or down.

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Describing translations

Q1: Mark the image, A’, of the point A under a translation equivalent to
moving 4 units to right followed by moving 3 units upward.

A’(image)

A © Boardworks Ltd 2009

(object)

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Describing translations

Q2: Mark the image, B’, of the point B under a translation equivalent to
moving 3 units to left followed by moving 5 units downward.

B (object)

B’(image) © Boardworks Ltd 2009

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Describing translations

Q3: Draw the image of line CD under a translation equivalent to moving
4 units to right followed by moving 1 units downward.

D

C D’

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Translations on a coordinate grid

Q4:

C(–2, 6) y A(5, 7) The vertices of a
triangle lie on the
7 B(3, 2) points A(5, 7), B(3, 2)
6 1 2 3 4 5 6 7x and C(–2, 6).
5
4 A’(2, –1) Translate the shape 3
3 units left and 8 units
2 B’(0, –6) downward. Label each
1 point in the image.

–7 –6 –5 –4 –3 –2 –1 0
–1

–2

C’(–5, –2) –3
–4

–5

–6

–7

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Translations on a coordinate grid

Q5:

y A’(3, 2) The coordinates of
1 2 3 4 5 6 7x vertex A of this shape
7 are (–4, –2).
6
5 When the shape is
4 translated the
3 coordinates of vertex A’
2 are (3, 2).
1
What translation will
–7 –6 –5 –4 –3 –2 –1 0 map the shape onto its
–1
image?
A(–4, –2) –2
–3 7 units right
4 units upward
–4

–5

–6

–7

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Translations on a coordinate grid

Q6: y The coordinates of
vertex A of this shape
A’(–3, 3) 7 are (3, –4).
6
5 When the shape is
4 translated the
3 coordinates of vertex A’
2 are(–3, 3).
1
What translation will
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7x map the shape onto its
–1 A(3, –4)
–2 image?
–3
–4 6 left
–5 7 up
–6
–7

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Quiz 1:

Q1: Mark the image P’, of the point P under a translation
equivalent to moving 5 units to right followed by moving 3
units downward.

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Quiz 1:

Q2: Mark the image Q’, of the point Q under a translation
equivalent to moving 4 units to left followed by moving 5 units
upward.

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Quiz 1:

Q3: Draw the image of line EF under a translation equivalent
to moving 4 units to right followed by moving 2 units upward.

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Quiz 1:

Q4: Draw the image of K under a translation equivalent to
moving 3 units to left followed by moving 2 units downward.

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Describing translations

Method 2: By VECTOR form

We can describe translations using vectors.

Moving to right / left
Positive : Move to right
Negative : Move to left

Moving upward / downward
Positive : Move upward
Negative : Move downward

For example, the vector 3 describes a translation moving 3
–4
right and 4 down.

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Describing translations

Q1: Plot the image of point E under the translation

E’

E

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Describing translations

Q2: Plot the image of point G under the translation

G’

G

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Describing translations

Q3: Draw the image of object H under the translation

Hint:
Choose a point to be translated.

B’

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Determine the coordinates under a translations

Q4: Determine the coordinates of image point E under the translation

E’ (4,6)

E(2,3)

The coordinate of image point E is (4,6).

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Determine the coordinates under a translations

Q5: Determine the coordinates of image point N under the translation

N(-2,2)

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Quiz 2:

Q1: Plot the image of point R under the translation

R’

R © Boardworks Ltd 2009

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Quiz 2:

Q2: Plot the image of point S under the translation

S

S’

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Quiz 2:

Q3: Determine the coordinates of image point T under the translation

T(-4,1)

T’(1,0)

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Quiz 2:

Q4: Determine the coordinates of image point U under the translation

U(1,3)

U’(1,-5)

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Determine the coordinates of the image

Alternatively, when the point (x,y) undergoes a translation , the image
of (x,y) is :

( x + a , y + b)

Look back Q4 ! The coordinate of object
E is (2, 3) and it is
E’ (4,6) translated by

E(2,3) The coordinate of image
E is

(2+2,3+3)

= ( 4 , 6)

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Determine the coordinates of the image

Q1: Determine the coordinate of image for the object (4,-5) under

translation (4,-5)

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Determine the coordinates of the image

Q2: Determine the coordinate of image for point K(-8, -6) under
translation

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Quiz 3:

Q1: Determine the coordinate of image for the object (8,-3) under
translation

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Quiz 3:

Q2: Determine the coordinate of image of W(-4 , -5) under translation

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Determine the coordinates of the object (Inverse of Translation)

An inverse translation maps the image that has been
translated back onto the original object.

What is the inverse of a translation 7 units
to the left and 3 units down?

The inverse is an equal move in the opposite direction.
That is, 7 units right and 3 units up.

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Determine the coordinates of the object (Inverse of Translation)

If (p,q) is the image of point (x,y) under a translation , then

Hence, if a point (p,q) is the image under translation ,

the object is (p-a, q-b).

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Quiz 4:

Q1: Determine the coordinates of the object for the image (5,-3) under
translation

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Determine the coordinates of the object

Q1: Determine the coordinates of the object for the image (-3,4)
under translation .

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Determine the coordinates of the object

Q2: Determine the coordinates of the object for the image (7,-5)
under translation .

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Quiz 4: . Determine

Q2: M(-8, -5) is the image of point N under translation
the coordinates of point N.

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Problem Solving

Q1: Using the same orientation with the diagram given,
determine the coordinate of the image of point (-3, 7).

i) Determine the translation that
mapped object P to P’.

P ii) Determine the coordinates of

image point (-3,7).

P’

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Problem Solving
Q2:
If M(-4,9) is mapped onto M’(5,-8) under a translation, find the
coordinates of image point K(7,-3) under the same translation.

i) Determine the translation that mapped object M to M’.

ii) Determine the coordinates of K’.

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