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Unit J2 Section 1
Translations

A translation moves all the points of an object in the same direction and the same distance. The diagram shows a translation.

Here every point has been moved 8 units to the right and 3 units up.

This translation is described by what is called a vector

Further work on vectors is in Strand J, Unit J3.

Worked Examples

1

Describe the translation which moves the shaded shape to each of the other shapes shown.

To move to A, the shaded shape is moved 6 units to the right (horizontally) and 3 units up (vertically).

This is described by the vector .

To obtain B, the shaded shape is moved 5 units to the right and 5 units down.

This is described by the vector .

To obtain C, the shaded shape is moved 3 units to the left and 4 units down.

This is described by the vector .

To obtain D, the shaded shape is moved 5 units to the left and then 3 units up.

This is described by the vector .
2

The shape shown in the diagram is to be translated using
the vector .

Draw the image obtained using this translation.

The vector describes a translation which moves an object 6 units to the right and 2 units down. This translation can be applied to each point of the original.

The points can then be joined to give the translated image.

Exercises

The shaded shape has been moved to each of the other positions shown by a translation. Give the vector used for each translation.

A:

B:

C:

D:

E:

F:

G:

Describe the translation which moves:

(a)
A → C
(b)
C → B
(c)
F → E
(d)
B → D
(e)
D → B
(f)
E → C
(g)
C → D
(h)
A → F

Draw the shape shown.

Translate using the vector .

Translate the image using the vector .

Which vector would be needed to translate the final image back to the position of the original?

(a)

Describe a translation which would move one A onto another A.

(b)

Describe any other translations which would move a letter onto the same letter in a different position.

E.g.

Draw a simple shape and translate it using the vector .

Then translate the image using the vector .

(a)

Which single translation would map the original shape to its final position?

(b)

Translate your shape using the vector . Then translate the image using the vector . Which single translation would move the original shape to its final position?

(c)

If a shape was translated using the vector and then the vector , which single translation would be equivalent?

The points A, B, C and D have coordinates (4, 7), (2, −6), (−3, −6) and (0, 7).

Find the vector which would be used to translate:

(a)
A to B
(b)
C to D
(c)
D to A
(d)
A to D.

Challenge!

1. By moving only one coin in the pattern shown, make one row and one column, each containing 5 coins.

2. Rearrange the 8 coins to form a square with 3 coins on each side. By rearranging 4 coins, make a square with 4 coins on each side.