The idea, step by step
Slides and flips
A translation slides every point the same distance in the same direction. To translate a triangle 2 right and 1 up, move each vertex that way and join the new vertices in the same order.
A reflection flips a shape over a mirror line. A point and its image lie at equal perpendicular distances on opposite sides of the line. Points already on the line stay fixed.
Turns need a centre
A rotation turns a shape about a stated centre. Include the amount and direction, such as a quarter turn clockwise about (3, 3). Tracing paper can help you turn the shape without stretching it.
All three transformations preserve lengths and angles. A reflection reverses orientation, whereas a translation does not. Transform every vertex, not just the corner nearest the origin.
A common trap
A rotation can be described just by saying “turn it”.
Instead: Specify the centre, the turn size and the direction. Different centres usually produce different images.
See the thinking
Translate all vertices
Translate A(1,1), B(2,1), C(1,3) by 2 right and 1 up.
- Add 2 to each x-coordinate.
- Add 1 to each y-coordinate, then join the new vertices.
Reflect a point
Reflect P(1,2) across the vertical mirror line x = 3.
- P is 2 squares left of the mirror.
- Put its image 2 squares right of the mirror, at the same height.
Check your understanding
Translate (4,2) by 1 left and 2 up.
Show answer
(3,4)
Subtract 1 from x and add 2 to y.
Your turn
6 questions · 10 marks · Work at your own pace.
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.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics 2026
Constructing grids; ordered coordinates; movement; translations/reflections/rotations; symmetry.
Official curriculum source ↗