Translations | Year 7 | Ascent Library

01 / LEARN

The idea, step by step

A translation is a slide

A translation moves every point the same distance in the same direction. The shape does not turn or flip. Its image has the same side lengths, angles and area as the original.

Describe the horizontal movement first and the vertical movement second. Right increases the x-coordinate; left decreases it. Up increases the y-coordinate; down decreases it. A prime, such as A′, names the image of A.

Move each coordinate separately

To move 4 units right and 2 units up, add 4 to each x-coordinate and add 2 to each y-coordinate. The same instruction must work for every vertex.

Check your image against the grid: a horizontal side should stay horizontal, and all corresponding vertices should have the same movement. Do not move only the first vertex and then guess the others.

(x, y) \mapsto (x + 4, y + 2)

A common trap

Moving one vertex 4 units but moving another by a different amount.

Instead: A translation has one movement instruction for the whole shape. Record the same change in x and y for every vertex.

02 / WORKED EXAMPLES

See the thinking

Example 1

A point crossing both axes

Move $P (- 2, 3)$ 5 units right and 4 units down.

Add 5 to the x-coordinate: $- 2 + 5 = 3$ .
Subtract 4 from the y-coordinate: $3 - 4 = - 1$ .
The horizontal and vertical movements are applied independently.

P^{'} (3, - 1)

Example 2

Translate all three vertices

Translate $A (- 3, - 1)$ , $B (- 1, - 1)$ and $C (- 2, 2)$ 4 units right and 2 units up.

$A^{'} = (- 3 + 4, - 1 + 2) = (1, 1)$ .
$B^{'} = (- 1 + 4, - 1 + 2) = (3, 1)$ .
$C^{'} = (- 2 + 4, 2 + 2) = (2, 4)$ .
Each vertex moved by the same amount, so the result is a translation.

A^{'} (1, 1), B^{'} (3, 1), C^{'} (2, 4)

Check your understanding

$Q (1, - 3)$ moves 2 units left and 5 units up. Where is its image?

Show answer

$Q^{'} (- 1, 2)$

The new coordinates are $1 - 2 = - 1$ and $- 3 + 5 = 2$ .

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Translate $(2, 1)$ 3 units left and 4 units up.
2 marks
Translate $(- 4, - 2)$ 5 units right and 1 unit down.
2 marks
$A (- 1, 2)$ is translated to $A^{'} (3, - 1)$ . Describe the translation.
2 marks
Translate $A (- 3, 0)$ , $B (- 1, 0)$ and $C (- 2, 3)$ 2 units right and 2 units down. Give all image coordinates. Draw and label the image on the supplied grid.
3 marks
After moving 3 units right and 2 units up, a point is at $(5, 1)$ . Find its original coordinates.
2 marks
A student maps $A (0, 0)$ to $(2, 1)$ and $B (3, 0)$ to $(6, 1)$ . Can this be one translation? Explain.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Translate $(2, 1)$ 3 units left and 4 units up.
2 marks
$2 - 3 = - 1$ ; $1 + 4 = 5$ .
$(- 1, 5)$
Translate $(- 4, - 2)$ 5 units right and 1 unit down.
2 marks
$- 4 + 5 = 1$ ; $- 2 - 1 = - 3$ .
$(1, - 3)$
$A (- 1, 2)$ is translated to $A^{'} (3, - 1)$ . Describe the translation.
2 marks
The change in x is $3 - (- 1) = 4$ .
The change in y is $- 1 - 2 = - 3$ .
4 units right and 3 units down.
Translate $A (- 3, 0)$ , $B (- 1, 0)$ and $C (- 2, 3)$ 2 units right and 2 units down. Give all image coordinates. Draw and label the image on the supplied grid.
3 marks
Add 2 to each x-coordinate and subtract 2 from each y-coordinate.
$A^{'} (- 1, - 2), B^{'} (1, - 2), C^{'} (0, 1)$
After moving 3 units right and 2 units up, a point is at $(5, 1)$ . Find its original coordinates.
2 marks
Undo the movement: $5 - 3 = 2$ and $1 - 2 = - 1$ .
$(2, - 1)$
A student maps $A (0, 0)$ to $(2, 1)$ and $B (3, 0)$ to $(6, 1)$ . Can this be one translation? Explain.
2 marks
Compare the changes for both vertices.
One translation must give the same change for every point.
No. A moves 2 right and 1 up, but B moves 3 right and 1 up.

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Curriculum reference & lesson scope

Australian Curriculum v9 / South Australian Curriculum

Translations; reflections in coordinate axes; rotations about a point; recording transformations with coordinates; sequences of transformations; explaining what stays unchanged.

Official curriculum source ↗

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