Compare the shapes to identify the transformation type
The shape is the same size, so it is not an enlargement
Step 2
Identify the mirror line
x = 0 (the y-axis) maps (1, y) to (−1, y) for all y
Step 3
State the full description
Reflection in the line x = 0
Watch out
Watch out
Students say 'reflected in the y-axis' without writing the equation of the mirror line
f
Translation
Add the movement vector to every point.
f
Enlargement
Distance from centre is multiplied by the scale factor.
Worked example
Describe fully the single transformation that maps shape A at (1,1),(3,1),(3,4) to shape B at (−1,1),(−3,1),(−3,4).
1
Compare the shapes to identify the transformation type: The shape is the same size, so it is not an enlargement.Coordinates: x-values have changed sign, y-values unchanged → reflection.
2
Identify the mirror line: x = 0 (the y-axis) maps (1, y) to (−1, y) for all y.
3
State the full description: Reflection in the line x = 0.
Final answer
Reflection in the line x = 0 (the y-axis)
Question ladder
Build up to the hardest questions
Do them in order. If you miss a step, read the solution, then redo the question without looking.
Workedreasoning
Describe fully the single transformation that maps shape A at (1,1),(3,1),(3,4) to shape B at (−1,1),(−3,1),(−3,4).
3 marks4 minstransformations-worked
Show solution
Worked solution
1.Compare the shapes to identify the transformation type: The shape is the same size, so it is not an enlargement.Coordinates: x-values have changed sign, y-values unchanged → reflection.
2.Identify the mirror line: x = 0 (the y-axis) maps (1, y) to (−1, y) for all y.
3.State the full description: Reflection in the line x = 0.
Final answer
Reflection in the line x = 0 (the y-axis)
Mark points
M1: compare the shapes to identify the transformation type
M1: identify the mirror line
M1: state the full description
A1: Reflection in the line x = 0 (the y-axis)
Watch out
Students say 'reflected in the y-axis' without writing the equation of the mirror line. g. x = 0, y = x, y = −x).Similarly, for a rotation always state: centre, angle, and direction (clockwise or anticlockwise).
Diagnosticrecall
Describe the transformation: (2,3) maps to (2,−3).
1 mark2 minstransformations-q1
Show solution
Worked solution
1.Spot the skill: Four transformations: reflection (mirror line), rotation (centre, angle, direction), translation (vector), enlargement (centre, scale factor).
2.Use the compare the shapes to identify the transformation type stage first, then identify the mirror line.
3.Keep the final answer visible: Reflection in the x-axis (y = 0).
Final answer
Reflection in the x-axis (y = 0)
Mark points
M1: use the correct four transformations: reflection (mirror line), rotation (centre, angle, direction), translation (vector), enlargement (centre, scale factor).'describe fully' requires all details — one missing detail loses marks.
A1: Reflection in the x-axis (y = 0)
Watch out
Students say 'reflected in the y-axis' without writing the equation of the mirror line. g. x = 0, y = x, y = −x).Similarly, for a rotation always state: centre, angle, and direction (clockwise or anticlockwise).
Easyprocedure
A shape is rotated 90° clockwise about (0,0). Point (3,2) maps to where?
2 marks3 minstransformations-q2
Show solution
Worked solution
1.Spot the skill: Four transformations: reflection (mirror line), rotation (centre, angle, direction), translation (vector), enlargement (centre, scale factor).
2.Use the identify the mirror line stage first, then state the full description.
3.Keep the final answer visible: (2, −3).
Final answer
(2, −3)
Mark points
M1: use the correct four transformations: reflection (mirror line), rotation (centre, angle, direction), translation (vector), enlargement (centre, scale factor).'describe fully' requires all details — one missing detail loses marks.
A1: (2, −3)
Watch out
Students say 'reflected in the y-axis' without writing the equation of the mirror line. g. x = 0, y = x, y = −x).Similarly, for a rotation always state: centre, angle, and direction (clockwise or anticlockwise).
Mediumreasoning
Translate (4,1) by vector (−3, 5).
3 marks4 minstransformations-q3
Show solution
Worked solution
1.Spot the skill: Four transformations: reflection (mirror line), rotation (centre, angle, direction), translation (vector), enlargement (centre, scale factor).
2.Use the state the full description stage first, then compare the shapes to identify the transformation type.
3.Keep the final answer visible: (1, 6).
Final answer
(1, 6)
Mark points
M1: use the correct four transformations: reflection (mirror line), rotation (centre, angle, direction), translation (vector), enlargement (centre, scale factor).'describe fully' requires all details — one missing detail loses marks.
A1: (1, 6)
Watch out
Students say 'reflected in the y-axis' without writing the equation of the mirror line. g. x = 0, y = x, y = −x).Similarly, for a rotation always state: centre, angle, and direction (clockwise or anticlockwise).
Hardproblem solving
An enlargement scale factor 3 centred at (0,0) maps (2,1) to where?
3 marks5 minstransformations-q4
Show solution
Worked solution
1.Spot the skill: Four transformations: reflection (mirror line), rotation (centre, angle, direction), translation (vector), enlargement (centre, scale factor).
2.Use the compare the shapes to identify the transformation type stage first, then identify the mirror line.
3.Keep the final answer visible: (6, 3).
Final answer
(6, 3)
Mark points
M1: use the correct four transformations: reflection (mirror line), rotation (centre, angle, direction), translation (vector), enlargement (centre, scale factor).'describe fully' requires all details — one missing detail loses marks.
A1: (6, 3)
Watch out
Students say 'reflected in the y-axis' without writing the equation of the mirror line. g. x = 0, y = x, y = −x).Similarly, for a rotation always state: centre, angle, and direction (clockwise or anticlockwise).
Exam-stylemulti-step
Describe the transformation that maps (1,2) to (−2,1).
4 marks6 minstransformations-q5
Show solution
Worked solution
1.Spot the skill: Four transformations: reflection (mirror line), rotation (centre, angle, direction), translation (vector), enlargement (centre, scale factor).
2.Use the identify the mirror line stage first, then state the full description.
3.Keep the final answer visible: Rotation 90° anticlockwise about the origin.
Final answer
Rotation 90° anticlockwise about the origin
Mark points
M1: use the correct four transformations: reflection (mirror line), rotation (centre, angle, direction), translation (vector), enlargement (centre, scale factor).'describe fully' requires all details — one missing detail loses marks.
A1: Rotation 90° anticlockwise about the origin
Watch out
Students say 'reflected in the y-axis' without writing the equation of the mirror line. g. x = 0, y = x, y = −x).Similarly, for a rotation always state: centre, angle, and direction (clockwise or anticlockwise).
Grade 9 stretchproblem solving
Point A is (3, -1). It is enlarged by scale factor -2 about the origin. Find the image of A.
originAimagek=−2
4 marks7 minstransform-g9
Show solution
Worked solution
1.Multiply both coordinates by -2.
2.Check the image is on the opposite side of the centre.
Final answer
(-6, 2)
Mark points
M1: multiply each coordinate by -2
A1: (-6, 2)
Watch out
Do not rush straight into arithmetic. Select the relevant method and show a complete chain of working.
Timed checkpoint
12 mins - 9 marks
Switch between skills
Set a timer and attempt all four questions before opening any answers. This is closer to the way skills appear in a real paper.
1Transformations - 2 marksDescribe the transformation: (2,3) maps to (2,−3).Mark answer
Answer
Reflection in the x-axis (y = 0)
2Angles, lines and polygons - 2 marksThe exterior angle of a regular polygon is 24°. How many sides?Mark answer
Answer
15
3Properties of shapes - 2 marksName all 2D shapes with equal diagonals that bisect each other.Mark answer
Answer
Rectangle, square
4Perimeter, area and volume - 3 marksFind the perimeter of a rectangle with length 13 cm and width 8 cm.Mark answer
Answer
42 cm
Mastery check
I can explain the method for transformations.
I can show clear working without skipping key steps.
I can avoid this mistake: Students say 'reflected in the y-axis' without writing the equation of the mirror line. g.x = 0, y = x, y = −x).Similarly, for a rotation always state: centre, angle, and direction (clockwise or anticlockwise).
This guide follows the OCR GCSE Mathematics J560 specification. Practice questions are original Learnova questions shaped around official content and exam skills.