Translations/reflections/rotations | Year 5

01 / LEARN

Understand the idea.

Slides and flips

A translation slides every point the same distance in the same direction. Move each vertex using the same instruction, then join the images in the original order. The shape keeps its size and orientation.

A reflection flips across a mirror line. Each point and its image are equally far from the line on opposite sides, measured at right angles. Points already on the mirror line stay fixed.

An equal-unit coordinate grid labelled from zero to six on both axes, with triangle vertices A at (1, 1), B at (2, 1) and C at (1, 3). The translated image is not drawn.

Turns need a centre

A rotation turns around a fixed centre. Specify the centre, turn size and direction, such as a quarter turn clockwise about $(3, 3)$ . The centre stays fixed while the other points move around it.

Translations, reflections and rotations preserve lengths and angles. A reflection reverses orientation. Check every vertex: transforming just one corner gives too little information to draw the whole image correctly.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Translate all vertices

Translate A(1,1), B(2,1), C(1,3) by 2 right and 1 up.

Worked solution

1
Move A two right and one up.
$\begin{aligned} x & = 1 + 2 = 3 \\ y & = 1 + 1 = 2 \\ A^{'} & = (3, 2) \end{aligned}$
The translation adds two horizontally and one vertically.
2
Apply the same move to B.
$\begin{aligned} x & = 2 + 2 = 4 \\ y & = 1 + 1 = 2 \\ B^{'} & = (4, 2) \end{aligned}$
Every vertex must move by the same amounts.
3
Apply the same move to C.
$\begin{aligned} x & = 1 + 2 = 3 \\ y & = 3 + 1 = 4 \\ C^{'} & = (3, 4) \end{aligned}$
The instruction changes position without changing the triangle dimensions.
4
Join the three image vertices.
Joining A-prime, B-prime and C-prime in the original order completes the translated triangle.

Answer

A′(3,2), B′(4,2), C′(3,4).

EXAMPLE 02

Reflect a point

Reflect P(1,2) across the vertical mirror line x = 3.

An equal-unit coordinate grid labelled from zero to six on both axes, with point P at (1, 2) and a gold dashed vertical mirror line at x equals 3. The reflected image is not drawn.

Worked solution

1
Find the distance to the mirror.
$3 - 1 = 2 units$
P lies two horizontal units to the left of the vertical line x = 3.
2
Locate the matching distance on the other side.
$3 + 2 = 5$
Reflection places the image equally far to the right of the mirror.
3
Keep the height and write the image.
$P^{'} = (5, 2)$
A vertical mirror changes the horizontal position while preserving the vertical coordinate.

Answer

P′(5,2).

03 / YOUR TURN

Try it yourself.

Check your understanding

Translate (4,2) by 1 left and 2 up.

Show answer & reasoning

(3,4)

One left changes $x$ to $4 - 1 = 3$ ; two up changes $y$ to $2 + 2 = 4$ . The translated point is $(3, 4)$ .

Keep practising

6 worksheet questions · 10 marks

Open worksheet Worked solutions

Read the questions online

Translate $P (2, 3)$ by 3 right and 1 down.
1 mark
Reflect $P (2, 5)$ across $x = 3$ . Give its image coordinates.
1 mark
Reflect $Q (4, 1)$ across $y = 3$ . Give its image coordinates.
1 mark
Rotate $P (2, 4)$ a quarter turn clockwise about $C (3, 3)$ . Find its image.
2 marks
Translate $A (1, 1)$ , $B (2, 1)$ , $C (1, 3)$ by 1 right and 2 up. Give all image coordinates.
3 marks
A pupil moves two triangle corners 2 right but the third corner 3 right. Is this a translation of the whole triangle? Explain.
2 marks

Read the worked solutions

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

Translate $P (2, 3)$ by 3 right and 1 down.
1 mark
$2 + 3 = 5$ ; $3 - 1 = 2$ .
$(5, 2)$
Reflect $P (2, 5)$ across $x = 3$ . Give its image coordinates.
1 mark
P is 1 left of the mirror, so its image is 1 right at the same height.
$(4, 5)$
Reflect $Q (4, 1)$ across $y = 3$ . Give its image coordinates.
1 mark
Q is 2 below the mirror, so its image is 2 above it.
$(4, 5)$
Rotate $P (2, 4)$ a quarter turn clockwise about $C (3, 3)$ . Find its image.
2 marks
The offset from C is 1 left and 1 up. A clockwise quarter turn changes this to 1 right and 1 up.
$(4, 4)$
Translate $A (1, 1)$ , $B (2, 1)$ , $C (1, 3)$ by 1 right and 2 up. Give all image coordinates.
3 marks
Move all three points by the same amounts.
$A^{'} (2, 3)$ , $B^{'} (3, 3)$ , $C^{'} (2, 5)$ .
A pupil moves two triangle corners 2 right but the third corner 3 right. Is this a translation of the whole triangle? Explain.
2 marks
Moving one corner differently can change side lengths or the shape.
No. Every point must move by the same distance in the same direction.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics 2026

Constructing grids; ordered coordinates; movement; translations/reflections/rotations; symmetry.

Official curriculum source ↗

In this lesson

Understand the idea.

Slides and flips

Turns need a centre

See the method in action.

Translate all vertices

Move A two right and one up.

Apply the same move to B.

Apply the same move to C.

Join the three image vertices.

Reflect a point

Find the distance to the mirror.

Locate the matching distance on the other side.

Keep the height and write the image.

Try it yourself.

Check your understanding

Keep practising