The idea, step by step
Move one step at a time
A translation slides every point by the same amount. A reflection flips a shape in a stated mirror line. A rotation turns it about a stated centre, through a stated angle and direction. These moves preserve lengths and angles.
For a combined transformation, write the result after the first move before starting the next. The second instruction acts on that new image, not on the original shape again.
Order can change the result
Reflecting and then sliding does not usually finish at the same place as sliding and then reflecting. The mirror line or rotation centre remains fixed unless the instructions say otherwise.
Use named vertices or a simple corner to track the movement, then check the other vertices. The final image should be the same size and shape; only its position or orientation changes.
A common trap
Applying every instruction to the original shape separately.
Instead: Finish the first move, then apply the second move to its result. Keep the mirror or centre fixed.
See the thinking
Slide, then reflect
Triangle vertices are (1,1), (3,1) and (1,2). Slide 2 units right and 1 unit up. Then reflect in x = 3. Find the final vertices.
- After the slide: (3,2), (5,2), (3,3).
- Reflecting in x = 3 keeps (3,2) and (3,3) on the mirror.
- The point (5,2) is 2 units right of the mirror, so becomes (1,2), 2 units left.
Turn, then slide
A point is at (5,4). Rotate it 90° anticlockwise about (4,4), then slide 2 units left. Find the final point.
- The starting point is 1 unit to the right of the centre.
- A quarter-turn anticlockwise puts it 1 unit above the centre: (4,5).
- Slide 2 units left: (2,5).
Check your understanding
A point (2,1) moves 3 right and 2 up. Where is it?
Show answer
(5,3)
Add 3 to the horizontal coordinate and 2 to the vertical coordinate.
Your turn
6 questions · 13 marks · Work at your own pace.
Read the questions online
- Move point (1,2) 3 units right and 2 units up. Give its new coordinates.1 mark
- Reflect point (2,3) in the vertical line x = 4. Give its image.2 marks
- Rotate point (5,4) 90° anticlockwise about (4,4). Give the new point.2 marks
- Triangle vertices are (1,1), (3,1), (1,2). Slide 2 right and 1 up, then reflect in x = 3. Plot the final triangle.3 marks
- Start at (1,1). Plan A reflects in x = 3 then slides 2 right and 1 up. Plan B slides first, then reflects in x = 3. Find both final points.3 marks
- A triangle is reflected and then rotated. Name two measurements that remain unchanged.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Move point (1,2) 3 units right and 2 units up. Give its new coordinates.1 mark
1 + 3 = 4; 2 + 2 = 4.
(4,4) - Reflect point (2,3) in the vertical line x = 4. Give its image.2 marks
It is 2 units left of x = 4, so the image is 2 units right.
The height stays 3.
(6,3) - Rotate point (5,4) 90° anticlockwise about (4,4). Give the new point.2 marks
A point 1 right of the centre moves to 1 above it.
(4,5) - Triangle vertices are (1,1), (3,1), (1,2). Slide 2 right and 1 up, then reflect in x = 3. Plot the final triangle.3 marks
After sliding: (3,2), (5,2), (3,3).
Reflect across x = 3.
Final vertices: (3,2), (1,2), (3,3). - Start at (1,1). Plan A reflects in x = 3 then slides 2 right and 1 up. Plan B slides first, then reflects in x = 3. Find both final points.3 marks
A: (1,1) reflects to (5,1), then moves to (7,2).
B: (1,1) moves to (3,2), which lies on the mirror and stays fixed.
A: (7,2); B: (3,2). - A triangle is reflected and then rotated. Name two measurements that remain unchanged.2 marks
Both moves preserve size and shape.
Its position or orientation may change.
Its side lengths and angle sizes.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Year 6 prism cross-sections, combined transformations and tessellations, with visual reasoning.
Official curriculum source ↗