What does a child have to do to identify a geometric transformation in the 11+?

Identify the translation, rotation, or reflection relating a shape and its image. It is one of 55 named maths skills in the 11+, in the geometry strand, and this page carries 1 interactive exercise that practises it.

What is the trap in an 11+ identify a geometric transformation question?

A translation slides every corner the same distance in the same direction, so the shape is never turned or flipped over. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.

What is not part of identify a geometric transformation in the 11+?

The skill map draws the line here: Identifies the transformation from supplied figures or coordinates. It does not execute the transformation. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.

Which other 11+ skills should we practise alongside identify a geometric transformation?

The geometry strand holds 15 skills that are placed together on the skill map, and the pages next to identify a geometric transformation are plot or read a coordinate, preserve measure under a rigid transformation and reflect a coordinate. Each has its own exercise and its own link, and none of them needs an account.

How can my child practise identify a geometric transformation for free?

Use Which Card Was Played?, embedded on this page. It is the exercise the skill map attaches to identify a geometric transformation, it runs in the browser with no account to make, these exercises are not scored and do not save learner records. The separate quiz sends answers for marking and shows a score, without saving an assessment record. It also has its own link, so you can send it to a child without sending them anywhere else first.

Maths · Geometry

Identify a geometric transformation

Identify the translation, rotation, or reflection relating a shape and its image.

Watch the worked example

Slide, Turn, or Flip?

This video shows how to compare a shape and its image to identify the transformation that relates them. Watch an 11+ maths question solved step by step.

Open video page and transcript

Keep practising with Smart Cub Learning. Find topics to practise next

Quick quiz: Identify a geometric transformation

10 questions, with feedback after each one. No sign-up needed.

Read the questions in this quiz

Question 1
Triangle ABC is mapped onto A'(1, -1), B'(-3, 0), C'(3, 3). Rotations are about the origin. Which single transformation does this?
- A.Reflection in the y-axis
- B.Reflection in the x-axis
- C.Rotation of 90° clockwise
- D.Rotation of 90° anticlockwise
Question 2
Triangle ABC is mapped onto A'(3, -3), B'(2, 5), C'(-4, -1). Rotations are about the origin. Which single transformation does this?
- A.Reflection in the y-axis
- B.Rotation of 90° clockwise
- C.Rotation of 90° anticlockwise
- D.Reflection in the x-axis
Question 3
Triangle ABC is mapped onto A'(-5, 2), B'(5, 0), C'(4, -2). Rotations are about the origin. Which single transformation does this?
- A.Reflection in the y-axis
- B.Rotation of 90° anticlockwise
- C.Rotation of 90° clockwise
- D.Reflection in the x-axis
Question 4
Triangle ABC is mapped onto A'(2, -3), B'(-4, -1), C'(0, 2). Rotations are about the origin. Which single transformation does this?
- A.Rotation of 90° anticlockwise
- B.Reflection in the y-axis
- C.Rotation of 90° clockwise
- D.Reflection in the x-axis
Question 5
Triangle ABC is mapped onto A'(3, -4), B'(1, 2), C'(-4, 3). Rotations are about the origin. Which single transformation does this?
- A.Reflection in the x-axis
- B.Rotation of 90° anticlockwise
- C.Rotation of 90° clockwise
- D.Reflection in the y-axis
Question 6
Triangle ABC is mapped onto A'(3, -1), B'(3, 2), C'(-4, 4). Rotations are about the origin. Which single transformation does this?
- A.Reflection in the x-axis
- B.Reflection in the y-axis
- C.Rotation of 90° clockwise
- D.Rotation of 90° anticlockwise
Question 7
Triangle ABC is mapped onto A'(-1, 4), B'(0, -5), C'(4, 3). Rotations are about the origin. Which single transformation does this?
- A.Rotation of 90° anticlockwise
- B.Reflection in the y-axis
- C.Reflection in the x-axis
- D.Rotation of 90° clockwise
Question 8
Triangle ABC is mapped onto A'(-5, 0), B'(4, 2), C'(4, -4). Rotations are about the origin. Which single transformation does this?
- A.Reflection in the y-axis
- B.Rotation of 90° clockwise
- C.Reflection in the x-axis
- D.Rotation of 90° anticlockwise
Question 9
Triangle ABC is mapped onto A'(-1, 0), B'(5, 2), C'(-3, -4). Rotations are about the origin. Which single transformation does this?
- A.Rotation of 90° anticlockwise
- B.Rotation of 90° clockwise
- C.Reflection in the x-axis
- D.Reflection in the y-axis
Question 10
Triangle ABC is mapped onto A'(0, -1), B'(1, 2), C'(-1, 3). Rotations are about the origin. Which single transformation does this?
- A.Reflection in the x-axis
- B.Rotation of 90° clockwise
- C.Rotation of 90° anticlockwise
- D.Reflection in the y-axis

Practise it now

The move has already happened. Play each card on the outline and find the one that lands on the ghost exactly.

Loading the interactive exercise. Nothing you do here is saved or scored.

A worked example

One question of the kind this skill is tested with, worked all the way through: the reasoning, and what the wrong answers are there to catch.

Reading a transformation from the coordinates

Worked example: Triangle ABC is mapped onto A'(5, -3), B'(-5, 0), C'(1, 3). Rotations are about the origin. Which single transformation does this?

The original triangle and its coordinates are drawn above; the image coordinates are stated in the question.

Reflection in the x-axis
Reflection in the y-axis
Translation 3 right, 1 down
Rotation of 90° clockwise

Answer: Reflection in the y-axis

How you get there

Check every corner: A(-5, -3) → A'(5, -3); B(5, 0) → B'(-5, 0); C(-1, 3) → C'(1, 3). Each coordinate pair follows the rule for "Reflection in the y-axis", and the same rule works for all three corners, so that is the single transformation.

Why the other answers tempt

A translation slides every corner the same distance in the same direction, so the shape is never turned or flipped over.

If they are stuck, say this

Compare one corner with its image first, then test your choice on the other two corners. A slide moves every corner the same way, a flip across an axis changes the sign of just one coordinate, a half turn changes both signs, and a quarter turn swaps the two coordinates.

Now do it live in Which Card Was Played?

Kitchen-table script for parents

Try this together

A friendly mini script for the breakfast table, school run or a quiet two minutes. Read it aloud as written, or make it your own.

Ready? Let's try Identify a geometric transformation together. Take a look at the picture. Here is what matters: Geometry figure: triangle. Here comes the question: Worked example: Triangle ABC is mapped onto A'(5, -3), B'(-5, 0), C'(1, 3). Rotations are about the origin. Which single transformation does this? A handy clue is: A slide moves every corner the same way, a flip across an axis changes the sign of just one coordinate, a half turn changes both signs, and a quarter turn swaps the two coordinates. Nice work. Here is the thinking: Each coordinate pair follows the rule for "Reflection in the y-axis", and the same rule works for all three corners, so that is the single transformation. So our answer is: Reflection in the y-axis. One sneaky trap is: A translation slides every corner the same distance in the same direction, so the shape is never turned or flipped over. Can you show me the first move in your own words? No rush; one calm step is enough.

What this exercise is doing

Which Card Was Played?

The move has already happened. Play each card on the outline and find the one that lands on the ghost exactly.

The move was “Turn 90° anticlockwise about (-4, 2)”. The card beside it, “Turn 90° clockwise about (4, 3)”, is the same kind of move, so calling it a turn settles nothing: what has to be read is which way round it turns, and which point it turns about. It comes down to one corner. A starts at (-1, -3) and the ghost has it at (1, 5); the other card sends it to (-2, 8) instead. That card puts two corners on spots the ghost also covers, but with the wrong letters, which is why a matching spot is never enough on its own. That is the exam-safe method: settle what is different about the two cards, then pin it down with a single corner.

Step 1. Look at it. Drag the track to play a card and watch where the outline goes. Scrub back to try another.
Step 2. Name the move. Which card was played? Pick the one that lands the outline exactly on the ghost.

What to say if they get stuck

Both cards play the same kind of move, so deciding it was a turn does not choose between them. What is different is which way round it turns, and which point it turns about.
Follow one corner. A starts at (-1, -3) and the ghost has it at (1, 5), so the right card has to send it exactly there.
Check a second corner before you lock in. The wrong card here puts two corners on spots the ghost also covers, but each one carries the wrong letter, so check the letter as well as the spot.

Open Which Card Was Played? on its own page to share it

How identify a geometric transformation differs from the skills beside it

The same exercise practises several skills, and telling them apart is often the difficulty rather than the exercise itself. On this page the skill is: identify the translation, rotation, or reflection relating a shape and its image, and it stops where identifies the transformation from supplied figures or coordinates. It does not execute the transformation.

Reflect a shape
Identify the result of one reflection in a stated mirror line. Excludes rotation and translation.
Rotate a shape
Identify the result of one stated rotation. Centre, direction, and turn are fixed.

Related maths skills

Classify an angleClassify one angle by size or compare it with a reference turn.
Compose coordinate transformationsApply two stated coordinate transformations in order.
Identify a cube netDetermine whether a net folds to a cube.
Identify a shape propertyIdentify one stated property of a 2D or 3D shape.
Identify line symmetryIdentify or complete a reflection across one mirror line.
Plot or read a coordinateRead or place one point on a coordinate grid.
Preserve measure under a rigid transformationUse the fact that translation, rotation, and reflection preserve lengths and angles.
Reflect a coordinateDetermine a point image after reflection in a stated coordinate axis.
Rotate a coordinateDetermine a point image after a stated rotation about the origin.
Solve an angle relationCalculate one unknown angle using a stated line, point, triangle, or quadrilateral relation.

All maths 11+ skills

Questions parents ask about identify a geometric transformation

What this skill involves, common mistakes and ways to practise it at home.

: Identify the translation, rotation, or reflection relating a shape and its image. It is one of 55 named maths skills in the 11+, in the geometry strand, and this page carries 1 interactive exercise that practises it.
: A translation slides every corner the same distance in the same direction, so the shape is never turned or flipped over. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.
: Point at the next move rather than explaining the whole rule. Compare one corner with its image first, then test your choice on the other two corners. A slide moves every corner the same way, a flip across an axis changes the sign of just one coordinate, a half turn changes both signs, and a quarter turn swaps the two coordinates.
: The skill map draws the line here: Identifies the transformation from supplied figures or coordinates. It does not execute the transformation. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.
: The geometry strand holds 15 skills that are placed together on the skill map, and the pages next to identify a geometric transformation are plot or read a coordinate, preserve measure under a rigid transformation and reflect a coordinate. Each has its own exercise and its own link, and none of them needs an account.
: Use Which Card Was Played?, embedded on this page. It is the exercise the skill map attaches to identify a geometric transformation, it runs in the browser with no account to make, these exercises are not scored and do not save learner records. The separate quiz sends answers for marking and shows a score, without saving an assessment record. It also has its own link, so you can send it to a child without sending them anywhere else first.

Knowing which maths topic to practise is most of the work

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