Your learning journey
Transform points and shapes by translation, reflection and rotation, and describe each transformation completely.
Follow the task-specific calculator guidance in Apply. Keyboard - means the same as −. Attempt before opening a scaffold or intentional practice explanation.
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Ready.
Connect & Check
Object: starting shape. Image: transformed shape. Translation vector (a,b): move a horizontally, b vertically. Mirror line: reflection axis. Centre of rotation: fixed turning point.
Intentional practice feedback after your attempt
Left 2.
Then up 3.
Intentional practice feedback after your attempt
3.
Signed addition.
Intentional practice feedback after your attempt
90°.
One fourth of a full turn.
Present
Translation adds the same vector to every vertex. Reflection places each image the same perpendicular distance on the other side of the mirror. Rotation preserves distances from its centre and turns all points through the same directed angle. These three transformations preserve lengths and angles.
Plot vertices accurately; transform each one; join in the same order. Describe translation by a vector, reflection by a line equation, rotation by angle, direction and centre. Check lengths and orientation.
Optional scaffold
Horizontal then vertical.
Intentional practice feedback after your attempt
(3,1).
Add each component.
Optional scaffold
Equal distance either side of y-axis.
Intentional practice feedback after your attempt
(4,1).
Same y, x changes sign.
Optional scaffold
Count from the mirror, not origin.
Intentional practice feedback after your attempt
(−1,−1).
Each x is two units from 1.
Optional scaffold
Sketch or use tracing paper.
Intentional practice feedback after your attempt
(2,3).
Rule (x,y)→(−y,x) for this centre and direction.
Apply
Optional scaffold
Change one coordinate at a time.
Intentional practice feedback after your attempt
(5,−1); (2,2); (5,2).
Each vector acts on the original.
Intentional practice feedback after your attempt
A′(1,−1), B′(3,−1), C′(1,−2); AB=A′B′=2.
Reflection reverses vertical sign.
Intentional practice feedback after your attempt
Translation vector (−2,3).
All three displacements agree.
No calculator needed. Check each coordinate separately; use squared distance from the centre if verifying a rotation numerically, but do not rely on a single vertex to describe a whole shape.
Apply and extend
Intentional practice feedback after your attempt
No; its perpendicular distance is zero.
It is a fixed point.
Intentional practice feedback after your attempt
Clockwise (3,−2); anticlockwise (−3,2). They are different images.
A complete rotation description needs centre, angle and direction.
Access, Scaffold, Core and Stretch support the same goal. Stretch deepens reasoning for either qualification tier.
Recall & Review
Retrieval without notes
Six retrieval points. Enter a number, decimal, fraction such as 3/2, or mixed number such as 1 1/2. Equivalent numeric values are accepted. Unsupported notation goes to teacher review. For rounding, also communicate the requested accuracy in written work; numerical scoring cannot judge significant trailing zeros.
Not checked.
Independent exit evidence
P1–P2: five minutes, no notes, 4 marks. Your teacher reviews working and explanations. Full assessment solutions are not embedded.
Recall & Review and prepare
An enlargement multiplies every displacement from a fixed centre by a scale factor. It changes lengths by that factor while preserving shape. The centre need not be the origin.
Retrieve F1 again in one week. Bring your working and one question.
Higher alternative: Combining transformations
Higher route: replace the 2-minute A3 feedback and the two 4-minute Challenge discussions with this 10-minute taught extension. Retain core P1–P2. Set HX1–HX2 as the final four minutes of that alternative, and use the shared challenges later if needed. The core route remains 60 minutes; the extension is not an additional compulsory ten minutes. Route choice reflects tier curriculum, not temporary support needs.
Reflect P(2,3) in x=0: (−2,3). Then reflect in y=0: (−2,−3). For any point (x,y), the result is (−x,−y), equivalent to a 180° rotation about the origin. Reversing these two perpendicular-axis reflections gives the same result. This does not mean every pair of transformations can be reversed without changing the image.
Intentional Higher practice feedback
(−4,−1), then (−4,1).
Intentional Higher practice feedback
Translation then reflection: (4,2) then (−4,2). Reflection then translation: (−1,2) then (2,2). Different final images.
HX1–HX2: teacher review. Completion is not mastery.
Your progress summary
Completion records attempts, not mastery. Retrieval points describe the latest checked attempt. Your teacher reviews P1–P2 separately and checks retained understanding after a delay.
Restore a backup
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Optional extension activities
Allow 10–15 minutes if the main practice is secure. Show your method, explain a check and justify your conclusion.
Stretch
Reveal a worked check after attempting
Translation gives (2,−3); reflection gives (2,3).
Deep challenge
Reveal a worked check after attempting
No. Reflect (1,1) in y-axis then translate (2,0) gives (1,1); reverse order gives (−3,1).