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Translate an Object

In this worksheet, students will interpret and create vectors then use these to affect translations of points and shapes.

'Translate an Object' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Geometry and Measures, Congruence and Similarity

Curriculum subtopic:   Properties and Constructions, Plane Vector Geometry

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

In geometry, translation simply means moving without rotating, resizing or anything else.

It can be best summed up by the word: slide.

 

 

How do we describe a translation?

 

When we are translating an object, we need to know how far to move it.

We do this by saying how far right or left it needs to move, plus how far up or down it needs to move.

We describe this movement using a vector.

 

 

What is a vector?

 

A vector looks like this:

 

a
b

 

a defines the horizontal movement (left or right) and b defines the vertical movement (up or down).

If a is positive, the movement will be to the right and, if it is negative, it will be to the left.

If b is positive, the movement will be up and, if it is negative, it will be down.

 

 

Let's look at some examples:

 

4 4 right
5 5 up

 

3 3 right
-1 1 down

 

-2 2 left
0 no vertical movement

 

 

 

How do we move a shape?

 

The key thing to remember about translations is that every point of the shape must move the same distance and in the same direction.

So if we move each corner individually by the same distance and in the same direction, then we can rejoin the points and create the new shape. 

 

 

Let's look at these features and processes in action now in an example. 

 

 

 

e.g. Translate shape a by the vector: 

 

1
-4

 

 

This vector means we have to move the shape 1 square to the right and 4 squares down.

 

 

 

 

Let's put this process into action and try translating some points and shapes now. 

 

In this activity, we will interpret and create vectors then use these to affect translations of points and shapes, as shown in the method above. 

Which word from the options below best describes the action of translation?

Flip

Turn

Slide

A translation is always described using a vector in the form:

 

a
b

 

Which movement (either horizontal and vertical) does each letter describe? 

 

Write the word 'horizontal' or 'vertical' into each of the spaces in the statements below. 

Flip

Turn

Slide

What translation does this vector describe?

 

2
3

What translation does this vector describe?

 

3
-2

If a translation causes a movement of 5 squares to the right and 3 up, how would we express this as a vector? 

 

a
b

 

Do not use any spaces in your answer or you may be marked incorrectly. 

 Value
a =
b =

If a translation causes a movement of 2 squares to the left and 1 down, how would we express this as a vector? 

 

a
b

 

Do not use any spaces in your answer or you may be marked incorrectly. 

 Value
a =
b =

Review the triangle abc shown below:

 

Grid showing triangle abc

 

This triangle needs to be translated by the vector:

 

3
2

 

Once this translation has taken place, express the coordinates of point b'.

 

Type one number into each of the boxes below to express the coordinates of the point in the form (a,b)

 Value
a =
b =

Investigate triangle abc once more, shown below:

 

Grid showing triangle abc

 

This triangle needs to be translated by the vector:

 

-1
-2

 

 

Once this translation has taken place, express the coordinates of point c'.

 

Type one number into each of the boxes below to express the coordinates of this point in the form (a,b)

 Value
a =
b =

Review the five triangle labelled a-e depicted below:

 

Grid showing 5 triangles labelled a-e

 

One of these shapes has been translated from its original location using the vector:

 

2
-3

 

Which pair of shapes shown above were involved in this translation?

a

b

c

d

e

Again, explore the five triangle labelled a-e depicted below:

 

Grid showing 5 triangles labelled a-e

 

One of these shapes has been translated from its original location using the vector:

 

5
0

 

Which pair of shapes shown above were involved in this translation?

a

b

c

d

e

  • Question 1

Which word from the options below best describes the action of translation?

CORRECT ANSWER
Slide
EDDIE SAYS
Did you remember this link from the Introduction? Each of the transformations has a word that describes its use in simple terms: 'Flip' describes a reflection; 'Turn' describes a rotation; 'Slide' describes a translation. Let's put this into action in the rest of this activity now...
  • Question 2

A translation is always described using a vector in the form:

 

a
b

 

Which movement (either horizontal and vertical) does each letter describe? 

 

Write the word 'horizontal' or 'vertical' into each of the spaces in the statements below. 

CORRECT ANSWER
EDDIE SAYS
Vectors can be remembered using the same method as coordinates: "Along the corridor and up the stairs". Pulling out the key words along and up, tells us that a links to 'along' or the horizontal movement whilst b links to 'up' or the vertical movement.
  • Question 3

What translation does this vector describe?

 

2
3
CORRECT ANSWER
EDDIE SAYS
As both the numbers present are positive, we simply have to apply the vertical and horizontal movements to the correct numbers. 2 is in the a position, so it indicates the movement 2 squares to the right. 3 is in the b position, so it indicates the movement 3 squares up.
  • Question 4

What translation does this vector describe?

 

3
-2
CORRECT ANSWER
EDDIE SAYS
This time we have one positive movement present and one negative. A positive value indicates up and right, whilst negative indicates left and down. 3 is in the a position, so it indicates the movement 3 squares to the right. -2 is in the b position, so it indicates the movement 2 squares down.
  • Question 5

If a translation causes a movement of 5 squares to the right and 3 up, how would we express this as a vector? 

 

a
b

 

Do not use any spaces in your answer or you may be marked incorrectly. 

CORRECT ANSWER
 Value
a =
b =
EDDIE SAYS
Now we are working the opposite way - from movement to vector, rather than vector to movement. a expresses the horizontal movement; to the right if it has a positive value and to the left if it is negative. As the movement is "5 squares to the right", we would express a as 5. b expresses the vertical movement; upwards if it has a positive value and downwards if it is negative. As the movement is "3 squares up", we would express b as 3. So our total vector for this movement would be:
5
3
  • Question 6

If a translation causes a movement of 2 squares to the left and 1 down, how would we express this as a vector? 

 

a
b

 

Do not use any spaces in your answer or you may be marked incorrectly. 

CORRECT ANSWER
 Value
a =
b =
EDDIE SAYS
a expresses the horizontal movement; to the right if it has a positive value and to the left if it is negative. As the movement is "2 squares to the left", we would express a as -2. b expresses the vertical movement; upwards if it has a positive value and downwards if it is negative. As the movement is "1 square down", we would express b as -1. So our total vector for this movement would be:
-2
-1
  • Question 7

Review the triangle abc shown below:

 

Grid showing triangle abc

 

This triangle needs to be translated by the vector:

 

3
2

 

Once this translation has taken place, express the coordinates of point b'.

 

Type one number into each of the boxes below to express the coordinates of the point in the form (a,b)

CORRECT ANSWER
EDDIE SAYS
This vector means we have to move the shape 3 squares to the right and 2 squares up. Point b is currently at (6,4) so, if we move this point 3 to the right and 2 up, it will translate to (9,6).
  • Question 8

Investigate triangle abc once more, shown below:

 

Grid showing triangle abc

 

This triangle needs to be translated by the vector:

 

-1
-2

 

 

Once this translation has taken place, express the coordinates of point c'.

 

Type one number into each of the boxes below to express the coordinates of this point in the form (a,b)

CORRECT ANSWER
EDDIE SAYS
This vector means we have to move the shape 1 square to the left and 2 squares down. Point b is currently at (6,4) so, if we move this 1 to the left and 2 down, it will translate to (5,2).
  • Question 9

Review the five triangle labelled a-e depicted below:

 

Grid showing 5 triangles labelled a-e

 

One of these shapes has been translated from its original location using the vector:

 

2
-3

 

Which pair of shapes shown above were involved in this translation?

CORRECT ANSWER
c
d
EDDIE SAYS
This vector means we have to move an original shape 2 squares to the right and 3 squares down. So we need to be looking for two shapes which have a horizontal difference of 2 and a vertical difference of 3. The only options which fit this criteria are triangle c (as the original) and triangle d (as the translation). Did you spot that relationship?
  • Question 10

Again, explore the five triangle labelled a-e depicted below:

 

Grid showing 5 triangles labelled a-e

 

One of these shapes has been translated from its original location using the vector:

 

5
0

 

Which pair of shapes shown above were involved in this translation?

CORRECT ANSWER
b
d
EDDIE SAYS
This vector means we have to move an original shape 5 squares to the right only, with no vertical movement at all. So we need to be looking for two shapes which have a vertical difference of 5. The only options which fit this criteria are triangle b (as the original) and triangle d (as the translation). Congratulations! You can now interpret and create vectors, then use these to affect translations of points and shapes.
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